A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction-diffusion systems

Fuente: arXiv
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Hauptverfasser: Asante-Asamani, E. O., Kleefeld, A., Wade, B. A.
Format: Preprint
Veröffentlicht: 2024
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author Asante-Asamani, E. O.
Kleefeld, A.
Wade, B. A.
author_facet Asante-Asamani, E. O.
Kleefeld, A.
Wade, B. A.
contents 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 Padé (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.
format Preprint
id arxiv_https___arxiv_org_abs_2403_14777
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction-diffusion systems
Asante-Asamani, E. O.
Kleefeld, A.
Wade, B. A.
Numerical Analysis
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 Padé (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.
title A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction-diffusion systems
topic Numerical Analysis
url https://arxiv.org/abs/2403.14777