Two step Runge-Kutta-Nyström methods for oscillatory problems based on mixed polynomials

Abstract

We consider two step Runge-Kutta-Nyström methods for the numerical integration of y″ = f(x, y) having periodic or oscillatory solutions. We assume that the frequency w can be estimated in advance. Using the linear stage representation, we describe how to derive two step Runge-Kutta-Nyström methods which integrate trigonometric and mixed polynomials exactly. The resulting methods depend on the parameter v = wh, where h is the stepsize. © Springer-Verlag Berlin Heidelberg 2003.