An initial-boundary corrected splitting method for diffusion-reaction problems
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918194980061184 |
|---|---|
| author | Dang, Thi Tam Einkemmer, Lukas Ostermann, Alexander |
| author_facet | Dang, Thi Tam Einkemmer, Lukas Ostermann, Alexander |
| contents | Strang splitting is a widely used second-order method for solving diffusion-reaction problems. However, its convergence order is often reduced to order $1$ for Dirichlet boundary conditions and to order $1.5$ for Neumann and Robin boundary conditions, leading to lower accuracy and reduced efficiency. In this paper, we consider a new splitting approach, called an initial-boundary corrected splitting, which avoids order reduction while improving computational efficiency for a wider range of applications. In contrast to the corrections proposed in the literature, it does not require the computation of correction terms that depend on the boundary conditions and boundary data. Through rigorous analytical convergence analysis and numerical experiments, we demonstrate the improved accuracy and performance of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An initial-boundary corrected splitting method for diffusion-reaction problems Dang, Thi Tam Einkemmer, Lukas Ostermann, Alexander Numerical Analysis 65M12, 65M20, 65L04 Strang splitting is a widely used second-order method for solving diffusion-reaction problems. However, its convergence order is often reduced to order $1$ for Dirichlet boundary conditions and to order $1.5$ for Neumann and Robin boundary conditions, leading to lower accuracy and reduced efficiency. In this paper, we consider a new splitting approach, called an initial-boundary corrected splitting, which avoids order reduction while improving computational efficiency for a wider range of applications. In contrast to the corrections proposed in the literature, it does not require the computation of correction terms that depend on the boundary conditions and boundary data. Through rigorous analytical convergence analysis and numerical experiments, we demonstrate the improved accuracy and performance of the proposed method. |
| title | An initial-boundary corrected splitting method for diffusion-reaction problems |
| topic | Numerical Analysis 65M12, 65M20, 65L04 |
| url | https://arxiv.org/abs/2504.10125 |