An initial-corrected splitting approach for convection-diffusion-reaction problems

TL;DR

This paper introduces an initial-corrected splitting method for convection-diffusion-reaction problems that overcomes order reduction issues with Dirichlet boundary conditions, demonstrating second-order convergence through analysis and numerical tests.

Contribution

A novel initial-corrected splitting approach is proposed, achieving second-order convergence and effectively addressing order reduction in convection-diffusion-reaction problems with Dirichlet boundaries.

Findings

The method achieves second-order convergence.

Numerical experiments confirm improved performance.

Overcomes order reduction with Dirichlet boundary conditions.

Abstract

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.