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

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.