# A COMPARATIVE EXPLORATION ON DIFFERENT NUMERICAL METHODS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00001

#### Keywords:

Initial Value Problems (IVP),Euler’s Method,Modified Euler Method,Fourth-order Runge-Kutta Method,Error Estimation,

#### Abstract

In this paper, the initial value problem of Ordinary Differential Equations has been solved by using different Numerical Methods namely Euler’s method, Modified Euler method, and Runge-Kutta method. Here all of the three proposed methods have to be analyzed to determine the accuracy level of each method. By using MATLAB Programming language first we find out the approximate numerical solution of some ordinary differential equations and then to determine the accuracy level of the proposed methods we compare all these solutions with the exact solution. It is observed that numerical solutions are in good agreement with the exact solutions and numerical solutions become more accurate when taken step sizes are very much small. Lastly, the error of each proposed method is determined and represents them graphically which reveals the superiority among all the three methods. We fund that, among the proposed methods Runge-Kutta 4th order method gives the accurate result and minimum amount of error.

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