Analysis and Implementation of Adaptive Explicit Two-Step Methods

University essay from Lunds universitet/Matematik LTH

Abstract: Recently a new way of constructing variable step-size multistep methods has been proposed, that parametrizes the entire domain of multistep methods. In the presented work the case of explicit two-step methods is looked at, analyzed and related to the already known theory of multistep methods. The error coefficient is derived as a function of the step-size ratio and an upper limit to the method domain due to zero stability is found. The theory is used to introduce an implementation of a variable step-size methods from a pair of explicit two-step methods and optimal parameters then chosen empirically. The chosen method is tested on benchmark problems.

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