An initial-corrected splitting approach for convection-diffusion-reaction problems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929714111709184 |
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| author | Dang, Thi Tam Einkemmer, Lukas Ostermann, Alexander |
| author_facet | Dang, Thi Tam Einkemmer, Lukas Ostermann, Alexander |
| contents | Splitting methods constitute a well-established class of numerical schemes for solving convection-diffusion-reaction problems. They have been shown to be effective in solving problems with periodic boundary conditions. However, in the case of Dirichlet boundary conditions, order reduction has been observed even with homogeneous boundary conditions. In this paper, we propose a novel splitting approach, the so-called `initial-corrected splitting method', which succeeds in overcoming order reduction. A convergence analysis is performed to demonstrate second-order convergence of this modified Strang splitting method. Furthermore, we conduct numerical experiments to illustrate the performance of the newly developed splitting approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An initial-corrected splitting approach for convection-diffusion-reaction problems Dang, Thi Tam Einkemmer, Lukas Ostermann, Alexander Numerical Analysis 65M12, 65M20, 65L04 Splitting methods constitute a well-established class of numerical schemes for solving convection-diffusion-reaction problems. They have been shown to be effective in solving problems with periodic boundary conditions. However, in the case of Dirichlet boundary conditions, order reduction has been observed even with homogeneous boundary conditions. In this paper, we propose a novel splitting approach, the so-called `initial-corrected splitting method', which succeeds in overcoming order reduction. A convergence analysis is performed to demonstrate second-order convergence of this modified Strang splitting method. Furthermore, we conduct numerical experiments to illustrate the performance of the newly developed splitting approach. |
| title | An initial-corrected splitting approach for convection-diffusion-reaction problems |
| topic | Numerical Analysis 65M12, 65M20, 65L04 |
| url | https://arxiv.org/abs/2502.09371 |