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9. NUMERICAL METHODS FOR SOLVING FIRST ORDER INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATION USING PICARD’S, MODIFIED EULER AND RUNGE KUTTA METHODS by D.I. Lanlege, S. O. Momoh and A. Abubakar Volume 51 (May, 2019 Issue)
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NUMERICAL METHODS FOR SOLVING FIRST ORDER INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATION USING PICARD’S, MODIFIED EULER AND RUNGE KUTTA METHODS

D.I. Lanlege, S. O. Momoh and A. Abubakar

Department of Mathematical Science, Federal University Lokoja Kogi State, Nigeria.

Department of Mathematics/Computer Science, Ibrahim Badamasi Babangida University Lapai Niger State Nigeria.

Abstract

This research work mainly present Picard’s Method (PM), Modified Euler Method (MEM) and Runge Kutta Method (RKM) for solving first order initial value problems (IVP) in ordinary differential equations (ODEs). The three methods are practically well suited for solving numerical problems. In order to verify the efficiency and accuracy, we compare the numerical solutions with that of the exact solutions. Finally we investigate and compute the errors of the methods for different step size to examine superiority. The results show that the Runge Kutta Method is suitable for solving first order ordinary differential equation.

Keywords: Numerical Analysis, Ordinary Differential Equations(ODE),Numerical Solution, Exact Solution, Picard’s Method, Modified Euler Method and Runge Kutta Method.

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