Stability of ADI schemes applied to convection-diffusion equations with mixed derivative terms

K. J. in 't Hout, Bruno Welfert

Research output: Contribution to journalArticlepeer-review

72 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)19-35
Number of pages17
JournalApplied Numerical Mathematics
Volume57
Issue number1
DOIs
StatePublished - Jan 2007

Keywords

  • ADI splitting schemes
  • Convection-diffusion equations
  • Fourier transformation
  • Initial-boundary value problems
  • Numerical solution
  • Von Neumann stability analysis

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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