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Continuous Runge-Kutta-Nyström methods for initial value problems with periodic solutions

✍ Scribed by G. Papageorgiou; I.Th. Famelis

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
763 KB
Volume
42
Category
Article
ISSN
0898-1221

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✦ Synopsis

In the present work, we are concerned with the derivation of continuous Rung+Kutta-Nystrom methods for the numerical treatment of second-order ordinary differential equations with periodic solutions. Numerical methods used for solving such problems are better to have the characteristic of high phase-lag order. First we analyse the construction algorithm for a high phase-lag order scaled extension of an explicit Rung+Kutta-Nystrom method. Using this procedure, we manage to construct a phase-lag order 14 continuous extension of a popular nine stages 8(6) order ERKN pair. In the literature, only phsselag order 12 continuous extension of nine stages 8(6) ERKN pairs can be found, so the proposed scaling method has the higher, until now, dispersion order. Numerical tests for the proposed methods are done over various test problems.

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