Runge-Kutta(-Nystrom) 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 omega can be estimated in advance. The resulting methods depend on the parameter nu = omega h, 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. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.