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Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials

✍ Scribed by B. Paternoster

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
791 KB
Volume
28
Category
Article
ISSN
0168-9274

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✦ Synopsis

We consider the construction of Runge-Kutta(-Nyström) methods for ordinary differential equations whose solutions are known to be periodic. We assume that the frequency w tan be estimated in advance. The resulting methods depend on the Parameter v = wh, where h is the stepsize. Using the linear Stage representation of a Runge-Kutta method given in Albrecht's approach, we derive Runge-Kutta and Runge-Kutta-Nyström methods which integrate trigonometric polynomials exactly.

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