A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction-diffusion systems
Abstract
A fourth-order exponential time differencing (ETD) Runge-Kutta scheme with dimensional splitting is developed to solve multidimensional non-linear systems of reaction-diffusion equations (RDE). By approximating the matrix exponential in the scheme with the A-acceptable Pad\'e (2,2) rational function, the resulting scheme (ETDRK4P22-IF) is verified empirically to be fourth-order accurate for several RDE. The scheme is shown to be more efficient than competing fourth-order ETD and IMEX schemes, achieving up to 20 times speed in CPU time. Inclusion of up to three pre-smoothing steps of a lower order L-stable scheme facilitates efficient damping of spurious oscillations arising from problems with non-smooth initial/boundary conditions.
Cite
@article{arxiv.2403.14777,
title = {A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction-diffusion systems},
author = {E. O. Asante-Asamani and A. Kleefeld and B. A. Wade},
journal= {arXiv preprint arXiv:2403.14777},
year = {2024}
}
Comments
41 pages, 5 figures