Embedded pair of extended Runge–Kutta–Nyström type methods for perturbed oscillators

A 5(3) pair of extended Runge–Kutta–Nyström type methods for the numerical integration of perturbed oscillators is presented. These methods are based on the order conditions of extended Runge–Kutta–Nyström type methods proposed 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. Commun. 180 (2009) 1777–1794]. The numerical stability and phase properties of the fifth-order methods are analyzed. Numerical experiments are carried out to show the efficiency and robustness of our new methods in comparison with some well known high quality codes proposed in the scientific literature.