Efficient boundary corrected Strang splitting

TL;DR

This paper introduces three boundary correction methods for Strang splitting to prevent order reduction caused by complex boundary conditions, enhancing the accuracy of numerical solutions for evolution equations.

Contribution

It presents novel boundary correction techniques for Strang splitting applicable to various boundary conditions, improving its robustness and accuracy.

Findings

Effective boundary corrections prevent order reduction.

Numerical examples demonstrate improved accuracy.

Applicable to Dirichlet, Neumann, and mixed conditions.

Abstract

Strang splitting is a well established tool for the numerical integration of evolution equations. It allows the application of tailored integrators for different parts of the vector field. However, it is also prone to order reduction in the case of non-trivial boundary conditions. This order reduction can be remedied by correcting the boundary values of the intermediate splitting step. In this paper, three different approaches for constructing such a correction in the case of inhomogeneous Dirichlet, Neumann, and mixed boundary conditions are presented. Numerical examples that illustrate the effectivity and benefits of these corrections are included.