Abstract: In this paper a new embedded Singly Diagonally
Implicit Runge-Kutta Nystrom fourth order in fifth order method for
solving special second order initial value problems is derived. A
standard set of test problems are tested upon and comparisons on the
numerical results are made when the same set of test problems are
reduced to first order systems and solved using the existing
embedded diagonally implicit Runge-Kutta method. The results
suggests the superiority of the new method.
Abstract: In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.