Dice Question Streamline Icon: https://streamlinehq.com

Numerical solvers for high-frequency instabilities in go-or-grow systems

Investigate the feasibility of developing and validating numerical solvers that accurately resolve go-or-grow systems exhibiting high-frequency diffusion-driven instabilities, reliably distinguishing genuine model instabilities from discretization artefacts and identifying their sources.

Information Square Streamline Icon: https://streamlinehq.com

Background

The paper argues that coupled ODE–PDE go-or-grow systems can amplify high-frequency modes, rendering standard discretizations unreliable and potentially making accurate numerics inconceivable in some regimes.

The authors pose the unresolved problem of whether more sophisticated solvers can be designed to correctly capture and attribute observed instabilities, addressing a critical barrier to reliable simulation and validation.

References

While we have reviewed a wide array of analytical and numerical results concerning this special class of mathematical models, several important mathematical questions remain unresolved. Is it feasible to develop more sophisticated numerical solvers capable of correctly identifying the sources of the observed instabilities?

— Go-or-Grow Models in Biology: a Monster on a Leash (2412.05191 - Thiessen et al., 6 Dec 2024) in Section 8 (Discussion), Open Problems