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

被引：79

作者：

in 't Hout, K. J. ^{[1
]}

Welfert, B. D. ^{[1
]}

机构：

[1] Arizona State Univ, Dept Math & Stat, Tempe, AZ 85287 USA

来源：

APPLIED NUMERICAL MATHEMATICS | 2007年 / 57卷 / 01期

关键词：

initial-boundary value problems; convection-diffusion equations; numerical solution; ADI splitting schemes; Von Neumann stability analysis; Fourier transformation; DIRECTION IMPLICIT SCHEME; PARABOLIC EQUATIONS; CONTRACTIVITY; ACCURACY;

D O I：

10.1016/j.apnum.2005.11.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：19 / 35

页数：17