A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction-diffusion systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916171121426432 |
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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 |