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In this paper the unconditional stability of four well-known ADI schemes isanalyzed in the application to time-dependent multidimensional diffusionequations with mixed derivative terms. Necessary and sufficient conditions onthe parameter theta of each scheme are obtained that take into account theactual size of the mixed derivative coefficients. Our results generalizeresults obtained previously by Craig & Sneyd (1988) and In 't Hout & Welfert(2009). Numerical experiments are presented illustrating our main theorems.

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