Embedded explicit two-step Runge-Kutta-Nystrom for solving special second-order IVPs - Ariffin, L. M.; Senu, N.; Suleiman, M.; Majid, Z.A. (Hikari, 2014)
A third-order three-stage explicit Two-step Runge-Kutta-Nystr ̈om (TSRKN) method embedded into fourth-order three-stage TSRKN method is developed to solve special second-order initial value problems (IVPs) directly. The stability of the method is investigated. Numerical re-sults are obtained by solving a standard set of test problems, which then reduced to first-order system when solved using Runge-Kutta (RK) method and comparison are made with existing RK method with same order using variable step-size. The results clearly showed the advantage and the efficiency of the new method.