Abstract: This study is concerned with the approximate solution of the special second order initial value problem. For this purpose we use the s-stage (s = 2,3,4) Implicit Runge-Kutta methods of order 2s. Fourth order method is used by two iterative technique, perfect square iterative scheme and Cooper and Butcher iterative scheme while sixth and eighth order methods are solved by using Cooper and Butcher iterative scheme. We have converted the scheme in such a way that only two function evaluations are required per iteration for fourth order method, three for sixth order method and four for eighth order method. Finally we present the numerical results.