Error Estimation and Control for ODEs

Authors:
L. F. Shampine
Affiliations:
Mathematics Department, Southern Methodist University, Dallas, USA 75275
Venue:
Journal of Scientific Computing
Year:
2005

Citing 14
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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