Title
Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Amsterdam ,
Subject
Mathematics
Source (journal)
Applied numerical mathematics. - Amsterdam
Volume/pages
59(2009) :3/4 , p. 677-692
ISSN
0168-9274
ISI
000263527300022
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
We consider the unconditional stability of second-order ADI schemes in the numerical solution of finite difference discretizations of multi-dimensional diffusion problems containing mixed spatial-derivative terms. We investigate an ADI scheme proposed by Craig and Sneyd, an ADI scheme that is a modified version thereof, and an ADI scheme introduced by Hundsdorfer and Verwer. Both sufficient and necessary conditions are derived on the parameters of each of these schemes for unconditional stability in the presence of mixed derivative terms. Our main result is that, under a mild condition on its parameter è, the second-order Hundsdorfer and Verwer scheme is unconditionally stable when applied to semi-discretized diffusion problems with mixed derivative terms in arbitrary spatial dimensions k2.
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