Journal
APPLIED NUMERICAL MATHEMATICS
Volume 57, Issue 1, Pages 19-35Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.apnum.2005.11.011
Keywords
initial-boundary value problems; convection-diffusion equations; numerical solution; ADI splitting schemes; Von Neumann stability analysis; Fourier transformation
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We consider Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with cross derivative terms. We derive new linear stability results for three ADI schemes that have previously been studied in the literature. These results are subsequently used to show that the ADI schemes under consideration are unconditionally stable when applied to finite difference discretizations of general parabolic two-dimensional convection-diffusion equations. Supporting numerical evidence is included. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.
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