Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
139 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Novel Variants of Diffusive Representation of Fractional Integrals: Construction and Numerical Computation (2312.11305v1)

Published 18 Dec 2023 in math.NA and cs.NA

Abstract: In this paper, we revisit the diffusive representations of fractional integrals established in \cite{diethelm2023diffusive} to explore novel variants of such representations which provide highly efficient numerical algorithms for the approximate numerical evaluation of fractional integrals.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (16)
  1. Baffet, D. (2019). A Gauss-Jacobi kernel compression scheme for fractional differential equations. J. Sci. Comput., 79(1), 227–248.
  2. Approximation by exponential sums revisited. Appl. Comput. Harmon. Anal., 28(2), 131–149.
  3. Theory of Ordinary Differential Equations. McGraw-Hill, New York.
  4. Methods of numerical integration. Dover, Mineola, NY. Corrected reprint of the second (1984) edition.
  5. Diethelm, K. (2010). The analysis of fractional differential equations, volume 2004 of Lecture Notes in Mathematics. Springer, Berlin.
  6. Diethelm, K. (2022). A new diffusive representation for fractional derivatives, Part II: Convergence analysis of the numerical scheme. Mathematics, 10(8), 1245.
  7. Diethelm, K. (2023a). Diffusive representations for the numerical evaluation of fractional integrals. In 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA), 1–6. IEEE.
  8. Diethelm, K. (2023b). A new diffusive representation for fractional derivatives, Part I: construction, implementation and numerical examples. In A. Cardone, M. Donatelli, F. Durastante, R. Garrappa, M. Mazza, and M. Popolizio (eds.), Fractional differential equations, volume 50 of Springer INdAM Ser., 1–15. Springer, Singapore.
  9. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynam., 29, 3–22.
  10. Detailed error analysis for a fractional Adams method. Numer. Algorithms, 36(1), 31–52.
  11. Theory and applications of fractional differential equations, volume 204 of North-Holland Mathematics Studies. Elsevier, Amsterdam.
  12. Li, J.R. (2010). A fast time stepping method for evaluating fractional integrals. SIAM J. Sci. Comput., 31(6), 4696–4714.
  13. Lubich, C. (1985). Fractional linear multistep methods for Abel-Volterra integral equations of the second kind. Math. Comp., 45(172), 463–469.
  14. McLean, W. (2018). Exponential sum approximations for t−βsuperscript𝑡𝛽t^{-\beta}italic_t start_POSTSUPERSCRIPT - italic_β end_POSTSUPERSCRIPT. In Contemporary computational mathematics—a celebration of the 80th birthday of Ian Sloan, 911–930. Springer, Cham.
  15. Montseny, G. (1998). Diffusive representation of pseudo-differential time-operators. ESAIM Proc., 5, 159–175.
  16. Podlubny, I. (1999). Fractional Differential Equations. Academic Press, San Diego.

Summary

We haven't generated a summary for this paper yet.