Comments on "Embedded pair of extended Runge-Kutta-Nyström type methods for perturbed oscillators"

In a recent paper Fang [Embedded pair of extended Runge-Kutta-Nyström type methods for perturbed oscillators, Appl. Math. Modell. (2009), doi:10.1016/j.apm.2009.12.004] considered the embedded pair of extended Runge-Kutta-Nyström type methods for perturbed oscillators and analyzed numerical stability and phase properties of the methods. The authors claimed that their methods are based on the order conditions of extended Runge-Kutta-Nyström type methods presented by Yang et al. [Extended RKN-type methods for numerical integration of perturbed oscillators, Comput. Phys. Commun. 180 (2009) 1777-1794]. However, some careless mistakes have been made in that paper. For this reason we will make some comments on that paper.