Runge-Kutta(-Nystro¨m) methods for ODEs with periodic solutions based on trigonometric polynomials

We consider the construction of Runge-Kutta(-Nystrom) methods for ordinary differential equations whose solutions are known to be periodic. We assume that the frequency ω can be estimated in advance. The resulting methods depend on the parameter v = ωh, 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-Nystrom methods which integrate trigonometric polynomials exactly.

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