Comparison of Numerical Methods for System of First Order Ordinary Differential Equations

Abstract

In this paper three numerical methods are discussed to find the approximate solutions of a systems of first order ordinary differential equations. Those are Classical Runge-Kutta method, Modified Euler method and Euler method. For each methods formulas are developed for n systems of ordinary differential equations. The formulas explained by these methods are demonstrated by examples to identify the most accurate numerical methods. By comparing the analytical solution of the dependent variables with the approximate solution, absolute errors are calculated. The resulting value indicates that classical fourth order Runge-Kutta method offers most closet values with the computed analytical values. Finally from the results the classical fourth order is more efficient method to find the approximate solutions of the systems of ordinary differential equations.