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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 ω 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 = ωh, where h is the stepsize.

Two Step Runge-Kutta-Nyström Methods for Oscillatory Problems Based on Mixed Polynomials