Stability and convergence of the Peaceman-Rachford ADI method for initial-boundary value problems

Authors:
W. H. Hundsdorfer and J. G. Verwer

Journal:
Math. Comp. **53** (1989), 81-101

MSC:
Primary 65N40; Secondary 65M20

DOI:
https://doi.org/10.1090/S0025-5718-1989-0969489-7

MathSciNet review:
969489

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Abstract: In this paper an analysis will be presented for the ADI (alternating direction implicit) method of Peaceman and Rachford applied to initial-boundary value problems for partial differential equations in two space dimensions. We shall use the method of lines approach. Motivated by developments in the field of stiff nonlinear ordinary differential equations, our analysis will focus on problems where the semidiscrete system, obtained after discretization in space, satisfies a one-sided Lipschitz condition with a constant independent of the grid spacing. For such problems, unconditional stability and convergence results will be derived.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1989-0969489-7

Keywords:
Numerical analysis,
time-dependent PDE's,
alternating direction implicit methods,
Peaceman-Rachford method,
method of lines,
stability,
error bounds

Article copyright:
© Copyright 1989
American Mathematical Society