New explicit trigonometrically-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for periodic initial value problems - Demba, Musa Ahmed; Senu, Norazak; Ismail, Fudziah (Academic Publications, 2016)
In this work, we derive two new Runge-Kutta-Nyström (RKN) methods for solving periodic second order ordinary differential equations. We constructed these methods based on the RKN method of three-stage fourth-order derived by Garcia and RKN method of four-stage fifth-order derived by Hairer. The numerical results show that the efficiency of the new methods is more than the other existing methods.