BIT Numerical Mathematics

, Volume 38, Issue 4, pp 751–780

Convergence results for the MATLAB ode23 routine

  • H. Lamba
  • A. M. Stuart
Article

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).

AMS subject classification

34C35 65L07 65L20 65L50 

Key words

Error control adaptivity convergence tolerance proportionality 

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Copyright information

© Swets & Zeitlinger 1998

Authors and Affiliations

  • H. Lamba
    • 1
  • A. M. Stuart
    • 1
  1. 1.Scientific Computing and Computational Mathematics Program Division of Mechanics and ComputationStanford UniversityStanfordUSA

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