Solution of First Order Ordinary Differential Equations Using Fourth Order Runge-Kutta Method with MATLAB.

Abstract

Differential Equations are used in developing models in the physical sciences, engineering, mathematics, social science, environmental sciences, medical sciences and other numerous fields. This article examined solution of first ordinary differential equation using fourth order Runge-Kutta method with MATLAB. The fourth order Runge-Kutta method for modelling differential equations improves upon the Euler’s method to obtain a greater accuracy without the necessity for higher-order derivatives of the given function. A first order differential equation was solved using fourth order Runge-Kutta method with MATLAB and the same problem was solved analytically in order to obtain the exact solution. The MATLAB commands match up quickly with the steps of the fourth order Runge-Kutta algorithm. Slight variation of the MATLAB code was used to show the effect of the size of h on the accuracy of the solution (see figure 4.1, 4.2, 4.3).The MATLAB and exact solutions are approximately equal though the MATLAB approach is easier and faster. The obtained results are in agreement with those in existing literature and improved the results obtained by [1]