Oscillatory Stormer-Cowell methods

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:115

Article

van der Houwen, PJ ; Messina, E ; Sommeijer, BP

关键词: numerical analysis;    periodic problems;    Stormer-Cowell methods;    parallelism;   

DOI  :  10.1016/S0377-0427(99)00179-X

来源: Elsevier

【 摘 要 】

We consider explicit methods for initial-value problems for special second-order ordinary differential equations where the right-hand side does not contain the derivative of y and where the solution components are known to be periodic with frequencies omega(j) lying in a given nonnegative interval [(omega)under bar, (omega)over bar]. The aim of the paper is to exploit this extra information and to modify a given integration method in such a way that the method parameters are tuned to the interval [(omega)under bar, (omega)over bar]. Such an approach has already been proposed by Gautschi in 1961 fur linear multistep methods for first-order differential equations in which the dominant frequencies omega(j) are a priori known. In this paper, we only assume that the interval [(omega)under bar, (omega)over bar] is known. Two tuning techniques, respectively based on a least squares and a minimax approximation, are considered and applied to the classical explicit Stormer-Cowell methods and the recently developed parallel explicit Stormer-Cowell methods. (C) 2000 Elsevier Science B.V. All rights reserved.

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