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 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 θ of the scheme are derived concerning unconditional stability in the von Neumann sense.