A Comparative Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with Euler and Higher Order of Runge Kutta Methods using MATLAB

This paper was mainly present comparison to Euler method and fourth�order Runge Kutta Method (RK4) for solving initial value problems (IVP) for ordinary differential equations (ODE) using MATLAB. The two methods are quite efficient and practically well suited for solving this problem. To verify the accuracy, we can compare numerical solutions with the exact solutions using matlab. The numerical solutions are good agreement of the exact solutions. Numerical comparisons between Euler method and Runge Kutta method have been presented my MATLAB. We can compare the effort of such methods. In order to achieve higher accuracy in the solution, the step size needs to be very small. Finally we investigate and compute the errors of the two types of methods for different step sizes to examine superiority. Several numerical examples are given in this paper.