A Phase-Fitted Runge-Kutta-Nystr\"om method for the Numerical Solution of Initial Value Problems with Oscillating Solutions

A new Runge-Kutta-Nystr"om method, with phase-lag of order infinity, for the integration of second-order periodic initial-value problems is developed in this paper. The new method is based on the Dormand and Prince Runge-Kutta-Nystr"om method of algebraic order four\cite{pa}. Numerical illustrations indicate that the new method is much more efficient than the classical one.