A Runge-Kutta-Nyström pair for the numerical integration of perturbed oscillators

New Runge-Kutta-Nyström methods especially designed for the numerical integration of perturbed oscillators are presented in this paper. They are capable of exactly integrating the harmonic or unperturbed oscillator. We construct an embedded 4(3) RKN pair that is based on the FSAL property. The new method is much more efficient than previously derived RKN methods for some subclasses of problems.