Stability of ADI schemes for multidimensional diffusion equations with mixed derivative terms

In this paper the unconditional stability of four well-known ADI schemes is analyzed in the application to time-dependent multidimensional diffusion equations with mixed derivative terms. Necessary and sufficient conditions on the parameter θ of each scheme are obtained that take into account the actual size of the mixed derivative coefficients. Our results generalize results obtained previously by Craig & Sneyd (1988) and In ʼt Hout & Welfert (2009). Numerical experiments are presented illustrating our main theorems.