Accelerated Runge-Kutta Nystrom method for solving autonomous second-order ordinary differential equations y″ = f(y)

In this paper, the explicit Accelerated Runge-Kutta Nystrom (ARKN) method for numerical integration of autonomous second-order ordinary differential equations is developed. The method is two step in nature and requires less number of stages per step compared to the existing Runge-Kutta Nystrom (RKN) method. Algebraic order conditions of the method are obtained and ARKN methods of order three and four are derived. The stability of method is discussed and numerical results are given to illustrate the efficiency of the proposed method compared to existing RKN methods.