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Volume 9, Issue 2, April 2020, Page: 32-36
Comparison of Numerical Methods for System of First Order Ordinary Differential Equations
Jemal Demsie Abraha, Departiment of Mthematics, Wolaita Sodo University, Wolaita Sodo, Ethiopia
Received: Jan. 17, 2020;       Accepted: Feb. 26, 2020;       Published: Apr. 14, 2020
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.
Keywords
Euler Method, Modified Euler Method, Runge-Kutta Method, System of Ordinary Differential Equations
Jemal Demsie Abraha, Comparison of Numerical Methods for System of First Order Ordinary Differential Equations, Pure and Applied Mathematics Journal. Vol. 9, No. 2, 2020, pp. 32-36. doi: 10.11648/j.pamj.20200902.11
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