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

K. J. in 't Hout; Bruno Welfert

doi:10.1016/j.apnum.2005.11.011

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

K. J. in 't Hout, Bruno Welfert

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

82 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 language	English (US)
Pages (from-to)	19-35
Number of pages	17
Journal	Applied Numerical Mathematics
Volume	57
Issue number	1
DOIs	https://doi.org/10.1016/j.apnum.2005.11.011
State	Published - 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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10.1016/j.apnum.2005.11.011

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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.",

keywords = "ADI splitting schemes, Convection-diffusion equations, Fourier transformation, Initial-boundary value problems, Numerical solution, Von Neumann stability analysis",

author = "{in 't Hout}, {K. J.} and Bruno Welfert",

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N2 - 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.

AB - 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.

KW - ADI splitting schemes

KW - Convection-diffusion equations

KW - Fourier transformation

KW - Initial-boundary value problems

KW - Numerical solution

KW - Von Neumann stability analysis

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EP - 35

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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