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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Stability and convergence of the Peaceman-Rachford ADI method for initial-boundary value problems
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by W. H. Hundsdorfer and J. G. Verwer PDF
Math. Comp. 53 (1989), 81-101 Request permission

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
  • © Copyright 1989 American Mathematical Society
  • 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