TY  - JOUR
AU  - Kleefeld, Andreas
AU  - Asante-Asamani, E. O.
AU  - Wade, B. A.
TI  - A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction–diffusion systems
JO  - Journal of computational and applied mathematics
VL  - 465
SN  - 0771-050X
CY  - Amsterdam [u.a.]
PB  - North-Holland
M1  - FZJ-2025-01875
SP  - 116568
PY  - 2025
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001433835400001
DO  - DOI:10.1016/j.cam.2025.116568
UR  - https://juser.fz-juelich.de/record/1040395
ER  -