Abstract: Numerical solution methods of ordinary differential equations in numerical analysis is an important topic, which is usually used for many differential equations that is difficult to find their exact and analytic solution or the equation which cannot be represented in explicit form. There are many methods of numerical solution of ordinary differential equations such as; Taylor method, Euler method, Hunn method and Runge-Kutta method with first, second, third, fourth and higher orders respectively. Taylor's method is very accurate for numerical solution of differential equations, but it is rarely used because of the need for computations of successive derivatives. Euler's method has more errors but needs less computation. The Runge-Kutta method is a suitable and the most commonly used method with less computational steps and accurate calculation. The Runge-Kutta method is the generalized form of the Euler method which is used for numerical solution of ordinary differential equations. In this paper, the numerical solutions of ordinary differential equations are solved by Taylor, Euler and Runge-Kutta fourth-order methods and then their exact solutions are compared using tables and graphs.
Keywords: Ordinary Differential Equations, Numerical Solution of Equations, Exact Solution of Equations, Taylor’s Method, Euler’s Method, Runge-Kutta Method.
Title: Study of Numerical solution of Ordinary Differential Equation by Taylor, Euler and Runge-Kutta methods
Author: Sayed Abdul Bashir Osmani
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
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