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Runge_Kutta Method

Bushra H. Aliwi

Department of Mathematics

BABYLON UNIVERSITY

Introduction:-

        Here we will discus some methods for Solution of Ordinary Differential Equations (ODE) There are two types of conditions the first type is in Initial Value Problems that are specified at only one value of the independent variable that will use in the Rung_Kutta Method .

       The formula of Rung_Kutta Method is represent the fourth order formula for Taylar Series formula ( while the previous two methods which are Euler and Modified Euler are in reality first and second order ).This method requires four evaluation off to get more accurate results to closed to the exact solutions as we will see in the given example and the step size should be sufficiently small h=small number.

     Exercise were given for student to be solved by using this method and then compare the results with other methods the Euler and Euler modified   .