A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction-diffusion systems
<|reference_start|>A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction-diffusion systems: 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.<|reference_end|>
@article{asante-asamani2024a,
    title={A fourth-order exponential time differencing scheme with dimensional
  splitting for non-linear reaction-diffusion systems},
    author={E.O. Asante-Asamani, A. Kleefeld and B.A. Wade},
    journal={arXiv preprint arXiv:2403.14777},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.14777},
    primaryClass={math.NA cs.NA}
}