Waveform relaxation as a dynamical system
- Creators
- Bjørhus, Morten
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Stuart, Andrew M.
Abstract
In this paper the properties of waveform relaxation are studied when applied to the dynamical system generated by an autonomous ordinary differential equation. In particular, the effect of the waveform relaxation on the invariant sets of the flow is analysed. Windowed waveform relaxation is studied, whereby the iterative technique is applied on successive time intervals of length T and a fixed, finite, number of iterations taken on each window. This process does not generate a dynamical system on R+ since two different applications of the waveform algorithm over different time intervals do not, in general, commute. In order to generate a dynamical system it is necessary to consider the time T map generated by the relaxation process. This is done, and C^1-closeness of the resulting map to the time T map of the underlying ordinary differential equation is established. Using this, various results from the theory of dynamical systems are applied, and the results discussed.
Additional Information
© 1997 American Mathematical Society. Received by the editor December 19, 1994 and, in revised form, October 16, 1995. The first author was supported by the Research Council of Norway. The second author was supported by the National Science Foundation and the Office for Naval Research.Additional details
- Eprint ID
- 78126
- Resolver ID
- CaltechAUTHORS:20170612-145717225
- Research Council of Norway
- NSF
- Office of Naval Research (ONR)
- Created
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2017-06-12Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Other Numbering System Name
- Andrew Stuart
- Other Numbering System Identifier
- J35