Modified Douglas Splitting Methods for Reaction-Diffusion Equations

TL;DR

This paper introduces modified second-order Douglas splitting methods for reaction-diffusion equations, achieving second-order explicit inclusion while maintaining stability and convergence, and demonstrating improved efficiency over existing methods.

Contribution

The paper develops second-order explicit modifications to Douglas splitting methods, with proven stability and convergence for reaction-diffusion equations, enhancing computational efficiency.

Findings

Stability holds for key classes of reaction-diffusion equations.

Modified methods are often more efficient than existing approaches.

Second-order explicit inclusion preserves convergence properties.

Abstract

We present modifications of the second-order Douglas stabilizing corrections method, which is a splitting method based on the implicit trapezoidal rule. Inclusion of an explicit term in a forward Euler way is straightforward, but this will lower the order of convergence. In the modifications considered here, explicit terms are included in a second-order fashion. For these modified methods, results on linear stability and convergence are derived. Stability holds for important classes of reaction-diffusion equations, and for such problems the modified Douglas methods are seen to be often more efficient than related methods from the literature.