This work focuses on the numerical solution of ordinary differential equations in the absence of fluctuation. Here only the initial value problems are considered and the solutions are obtained over the unit interval [0, 1]. The main purpose of this work is to obtain a general procedure for the numerical solution of Ordinary Differential Equations. Although there are many methods for these problems, the method that we develop here has some impressive features. Numerical solution approximates to the exact solution rapidly without using too many mesh points.