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Convergence results for the MATLAB ODE23 routine

Lamba, H. and Stuart, A. M. (1998) Convergence results for the MATLAB ODE23 routine. BIT Numerical Mathematics, 38 (4). pp. 751-780. ISSN 0006-3835. https://resolver.caltech.edu/CaltechAUTHORS:20170609-154149149

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Abstract

We prove convergence results on finite time intervals, as the user-defined tolerance τ→0, for a class of adaptive timestepping ODE solvers that includes the ode23 routine supplied in MATLAB Version 4.2. In contrast to existing theories, these convergence results hold with error constants that are uniform in the neighbourhood of equilibria; such uniformity is crucial for the derivation of results concerning the numerical approximation of dynamical systems. For linear problems the error estimates are uniform on compact sets of initial data. The analysis relies upon the identification of explicit embedded Runge-Kutta pairs for which all but the leading order terms of the expansion of the local error estimate areO(∥f(u∥)^2).


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/BF02510413DOIArticle
https://link.springer.com/article/10.1007%2FBF02510413PublisherArticle
http://rdcu.be/tm0MPublisherFree ReadCube access
Additional Information:© 1998 Swets & Zeitlinger. Received 15 August 1997. Communicated by Stig Skelboe. This work was partially supported by NSF Grant DMS-95-04879.
Funders:
Funding AgencyGrant Number
NSFDMS-95-04879
Subject Keywords:Error control; adaptivity; convergence; tolerance proportionality
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ41
Issue or Number:4
Classification Code:AMS subject classification: 34C35; 65L07; 65L20; 65L50
Record Number:CaltechAUTHORS:20170609-154149149
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170609-154149149
Official Citation:Lamba, H. & Stuart, A.M. Bit Numer Math (1998) 38: 751. doi:10.1007/BF02510413
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78072
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Jun 2017 23:26
Last Modified:03 Oct 2019 18:05

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