Stability of ADI schemes for multidimensional diffusion equations with mixed derivative terms
KJ in ʼt Hout, C Mishra - Applied Numerical Mathematics, 2013 - Elsevier
Applied Numerical Mathematics, 2013•Elsevier
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.
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.
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 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.
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