On the stability of ADI methods

DAIMI Report Series

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Title On the stability of ADI methods
Creator Østerby, Ole
Description When solving parabolic equations in two space dimensions implicit methods are preferred to the explicit method because of their better stability properties. Straightforward implementation of implicit methods require time-consuming solution of large systems of linear equations, and ADI methods are preferred instead. We expect the ADI methods to inherit the stability properties of the implicit methods they are derived from, and we demonstrate that this is partly true. The Douglas-Rachford and Peaceman-Rachford methods are absolutely stable in the sense that their growth factors are ≤ 1 in absolute value. Near jump discontinuities, however, there are differences w.r.t. how the ADI methods react to the situation: do they produce oscillations and how effectively do they damp them. We demonstrate the behaviour on two simple examples.
Publisher Aarhus University
Date 2016-04-10
Type info:eu-repo/semantics/article
Peer-reviewed Article
Format application/pdf
Identifier http://ojs.statsbiblioteket.dk/index.php/daimipb/article/view/25146
Source DAIMI Report Series; No 598 (2016): PB-598 On the Stability of ADI Methods
DAIMI Report Series; No 598 (2016): PB-598 On the Stability of ADI Methods
Language eng
Relation http://ojs.statsbiblioteket.dk/index.php/daimipb/article/view/25146/22077
Rights Copyright (c) 2017 DAIMI Report Series

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