Journal Article

FZJ-2025-01875

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction–diffusion systems

Kleefeld, A.FZJ* ; Asante-Asamani, E. O. (Corresponding author) ; Wade, B. A.

2025
North-Holland Amsterdam [u.a.]

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Please use a persistent id in citations: doi:10.1016/j.cam.2025.116568  doi:10.34734/FZJ-2025-01875

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 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 20X speed-up 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.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)

Appears in the scientific report 2025

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Database coverage:
; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; Nationallizenz ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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