Stability of the Modified Craig-Sneyd scheme for two-dimensional convection-diffusion equations with mixed derivative term

TL;DR

This paper analyzes the stability of the Modified Craig-Sneyd scheme when applied to two-dimensional convection-diffusion equations with mixed derivatives, providing conditions for unconditional stability.

Contribution

It extends the MCS scheme to convection-diffusion equations with mixed derivatives and derives stability conditions for this extension.

Findings

Derived necessary and sufficient stability conditions

Established unconditional stability under certain parameters

Extended the applicability of the MCS scheme

Abstract

The Modified Craig-Sneyd (MCS) scheme is a promising splitting scheme of the ADI type introduced by In 't Hout & Welfert (2009) for multi-dimensional pure diffusion equations having mixed spatial-derivative terms.In this paper we investigate the extension of the MCS scheme to two-dimensional convection-diffusion equations with a mixed derivative. Both necessary and sufficient conditions on the parameter of the scheme are derived concerning unconditional stability in the von Neumann sense.