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Convergence and stability in the numerical approximation of dynamical systems

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
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.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-92-J-1876
NSFDMS-9201727
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartC6
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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