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. doi:10.1007/BF02510413. 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).
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Additional Information: | © 1998 Swets & Zeitlinger. Received 15 August 1997. Communicated by Stig Skelboe. This work was partially supported by NSF Grant DMS-95-04879. | ||||||||||||
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Subject Keywords: | Error control; adaptivity; convergence; tolerance proportionality | ||||||||||||
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Issue or Number: | 4 | ||||||||||||
Classification Code: | AMS subject classification: 34C35; 65L07; 65L20; 65L50 | ||||||||||||
DOI: | 10.1007/BF02510413 | ||||||||||||
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: | 15 Nov 2021 17:36 |
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