Abstract

Comparison of Higher Order Taylorís Method and Runge-Kutta Methods for Solving First Order Ordinary Differential Equations

Gashu Gadisa1 and Habtamu Garoma2

1,2Department of Mathematics, Jimma University, P.O. Box 378, Jimma, ETHIOPIA.

ABSTRACT

This paper mainly present, sixth order Taylorís method and fifth order Runge-Kutta method (RK5) for solving initial value problems of first order ordinary differential equations. The two proposed methods are quite efficient and practically well suited for solving these problems. In order to verify the accuracy, we compare numerical solutions with the exact solutions. The numerical solutions are in good agreement with the exact solutions. Numerical comparisons between Taylorís method and Runge-Kutta methods have been presented. The stability and convergence of the methods have been investigated. Two model examples (linear and non-linear) are given to demonstrate the reliability and efficiency of the methods. Point wise absolute errors are obtained by using MATLAB software. The proposed methods also compared with the existing literatures (RK4) and shows betterment results.

Keywords :Initial Value Problem, Taylor Series, Runge-Kutta Method, Stability Analysis.

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