An initial-boundary corrected splitting method for diffusion-reaction problems

Fuente: arXiv
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Hauptverfasser: Dang, Thi Tam, Einkemmer, Lukas, Ostermann, Alexander
Format: Preprint
Veröffentlicht: 2025
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_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