Extended RKN methods with FSAL property for oscillatory systems

In this paper, we present extended RKN methods with FSAL property for numerical integration of perturbed oscillators. These numerical integrators are based on the extended Runge–Kutta–Nyström-type methods proposed by Yang et al. [H.L. Yang, X.Y. Wu, Xiong 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 property of the new methods are analyzed. The paper is accompanied by numerical experiments that demonstrate the effectiveness and robustness of our new methods in comparison with some well-known methods appeared in the scientific literature.