Extended RKN-type methods with minimal dispersion error for perturbed oscillators

In this paper, extended Runge–Kutta–Nyström-type methods with minimal dispersion error for the numerical integration of perturbed oscillators are presented, which are based on the order conditions derived by Yang et al. (H.L. Yang, X.Y. Wu, X. You, Y.L. Fang, Extended RKN-type methods for numerical integration of perturbed oscillators, Comput. Phys. Comm. 180 (2009) 1777–1794). The numerical stability and phase properties of the new methods are analyzed. Numerical experiments are reported in comparison with some well-known high quality codes proposed in the scientific literature.