Modified Strang splitting for semilinear parabolic problems

TL;DR

This paper introduces a modified Strang splitting method to address order reduction issues in solving one-dimensional semilinear parabolic equations with Dirichlet boundary conditions, improving accuracy for such problems.

Contribution

The paper proposes a novel modification to the Strang splitting technique to prevent order reduction caused by boundary condition incompatibility.

Findings

The modified splitting maintains the expected order of accuracy.

Numerical experiments demonstrate improved solution accuracy.

Applicable to equations like the Burgers equation.

Abstract

We consider applying the Strang splitting to semilinear parabolic problems. The key ingredients of the Strang splitting are the decomposition of the equation into several parts and the computation of approximate solutions by combining the time evolution of each split equation. However, when the Dirichlet boundary condition is imposed, order reduction could occur due to the incompatibility of the split equations with the boundary condition. In this paper, to overcome the order reduction, a modified Strang splitting procedure is presented for the one-dimensional semilinear parabolic equation with first-order spatial derivatives, like the Burgers equation.