Comparision of Numerical Methods For Solving Initial Value Problem

Abstract

the researcher compere the accuracy of different methods, such as the Improved Euler, Runge-Kutta order four and Rung-Kutta Fehlberg methods with initial value problems the results obtained from MATLAB and compare by table and graph A number of numerical examples on the completion of initial value problems computerizations to compere the accuracy between the Improved Euler, Runge-Kutta order four and RungKutta Fehlberg methods. In addition accuracy is being pointed out through error. From the research result Improved Euler method has an error greater than Runge-Kutta order four method while the Runge-Kutta Fehlberg method less error than Runge-Kutta order four method. It can be conclude that Runge-Kutta order four method is more accurate than Improved Euler method but the Runge-Kutta Fehlberg method is slightly more accurate than Runge-Kutta forth order method.the Runge-Kutta Fehlberg method is a computational time very similar, slightly more accurate results with a much lower number of discretization steps, But the additional computational cost per step.