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

Hout, Karel in 't; Mishra, Chittaranjan

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

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Author(s): Karel in 't Hout , Chittaranjan Mishra

Publication date Created: 05 May 2012

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Abstract

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 theta 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 't Hout & Welfert (2009). Numerical experiments are presented illustrating our main theorems.