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Error estimation and control for ODEs

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Abstract

This article is about the numerical solution of initial value problems for systems of ordinary differential equations. At first these problems were solved with a fixed method and constant step size, but nowadays the general-purpose codes vary the step size, and possibly the method, as the integration proceeds. Estimating and controlling some measure of error by variation of step size/method inspires some confidence in the numerical solution and makes possible the solution of hard problems. Common ways of doing this are explained briefly in the article.

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  1. Mathematics Department, Southern Methodist University, 75275, Dallas, TX, USA

    L. F. Shampine

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Shampine, L.F. Error estimation and control for ODEs. J Sci Comput 25, 3–16 (2005). https://doi.org/10.1007/BF02728979

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  • DOI: https://doi.org/10.1007/BF02728979

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