A phase-fitted collocation-base Runge-Kutta-Nystrom method

We consider collocation-based Runge-Kutta-Nystrom methods with symmetric points and derive a three-stage method which results exact in phase for second order linear ODEs having a periodic or an oscillatory solution. We assume that the dominant frequency k can be estimated in advance; then the resulting method depends on the parameter theta = kh, where h is the stepsize. Due to its stability properties, the method is suitable to integrate systems which exhibits a moderate stiffness. The procedure can be easily generalized to derive phase-fitted RKN methods with an arbitrary high order.