Oscillatory Störmer–Cowell methods

✍ Scribed by P.J. van der Houwen; E. Messina; B.P. Sommeijer

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 187 KB
• Volume: 115
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00179-x

✦ Synopsis

We consider explicit methods for initial-value problems for special second-order ordinary di erential 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 ! j lying in a given nonnegative interval [ !; !]. 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 [!; !]. Such an approach has already been proposed by Gautschi in 1961 for linear multistep methods for ÿrst-order di erential equations in which the dominant frequencies ! j are a priori known. In this paper, we only assume that the interval [ !; !] is known. Two "tuning" techniques, respectively based on a least squares and a minimax approximation, are considered and applied to the classical explicit St ormer-Cowell methods and the recently developed parallel explicit St ormer-Cowell methods.