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

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 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 Albrechtʹs approach, we derive Runge-Kutta and Runge-Kutta-Nyström methods which integrate trigonometric polynomials exactly.