%0 Journal Article
%A Kleefeld, Andreas
%A Asante-Asamani, E. O.
%A Wade, B. A.
%T A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction–diffusion systems
%J Journal of computational and applied mathematics
%V 465
%@ 0771-050X
%C Amsterdam [u.a.]
%I North-Holland
%M FZJ-2025-01875
%P 116568
%D 2025
%X 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:001433835400001
%R 10.1016/j.cam.2025.116568
%U https://juser.fz-juelich.de/record/1040395