Stuart, Andrew (1997) Convergence and stability in the numerical approximation of dynamical systems. In: The State of the Art in Numerical Analysis. Oxford University Press , Oxford, pp. 145-169. ISBN 9780198500148. https://resolver.caltech.edu/CaltechAUTHORS:20170613-141546199
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Abstract
In this article we give an overview of the application of theories from dynamical systems to the analysis of numerical methods for initial-value problems. We start by describing the classical viewpoints of numerical analysis and of dynamical systems and then indicate how the two viewpoints can be merged to provide a framework for both the interpretation of data obtained from numerical simulations and the design of efficient numerical methods. This is done in Section 2.
| Item Type: | Book Section | ||||||
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| Additional Information: | © 1997 Oxford University Press. The author is grateful to the participants of the Geiranger, Norway "ODE to NODE" workshop of June 1995, where a preliminary version of this material was discussed and subsequently improved, and to Tony Humphries who made several valuable suggestions. The figures are taken from [13] and used with the permission of Cambridge University Press. This work was supported by the Office of Naval Research, grant number N00014-92-J-1876, and by the National Science Foundation, grant number DMS-9201727. | ||||||
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| Record Number: | CaltechAUTHORS:20170613-141546199 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170613-141546199 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 78173 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Tony Diaz | ||||||
| Deposited On: | 13 Jun 2017 21:25 | ||||||
| Last Modified: | 03 Oct 2019 18:06 |
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