Control Theory and the Numerical Solution of ODEs

The goal of this paper is to study the entire class of linear second order multi-point methods. We characterize, as a three parameter family, those methods with good numerical properties. We will examine the error analysis of the class of second order methods and will study in some detail the statistics of switching between two methods. We characterize the average value obtained by switching and construct the covariance matrix. Two examples are done in some detail.

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Published 1 January 2008