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In this paper, we consider fourth order Runge-Kutta method for solving ordinary differential equations in initial value problems. The proposed methods are quite efficient and are practically well suited for solving these problems. Several examples are presented to demonstrate the accuracy and easy implementation of the proposed methods. The results of numerical experiments are compared with the analytical solution and thereby gain some insight into the accuracy of proposed methods. Finally we investigate and compute the error of proposed methods. This counterintuitive result is analyzed in this paper.

Accurate Solutions of Initial Value Problems for Ordinary Differential Equations with the Fourth Order Runge Kutta Method