Error Estimation and Control for ODEs

This article is about the numerical solution of initial value problems for systems of ordinary differential equations (ODEs). 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. Running Title: Error Estimation