A new family of Runge-Kutta type methods for the numerical integration of perturbed oscillators

Our task in this paper is to present a new family of methods of the Runge-K utta type for the numerical integration of perturbed oscillators. The key p roperty is that those algorithms are able to integrate exactly, without tru ncation error, harmonic oscillators, and that, for perturbed problems the l ocal error contains the perturbation parameter as a factor. Some numerical examples show the excellent behaviour when they compete with Runge-Kutta-Ny strom type methods.