A phase-fitted Runge–Kutta–Nyström method for the numerical solution of initial value problems with oscillating solutions

A new Runge–Kutta–Nyström 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, El-Mikkawy and Prince Runge–Kutta–Nyström method of algebraic order four with four (three effective) stages. Numerical illustrations indicate that the new method is much more efficient than other methods derived, based on the idea of minimal phase lag or of phase lag of order infinity.