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