Analysis and Comparative Study of Numerical Solutions of Initial Value Problems (IVP) in Ordinary Differential Equations (ODE) With Euler and Runge Kutta Methods

摘要

In this paper, we present Euler’s method and fourth-order Runge Kutta Method (RK4) in solvinginitial value problems (IVP) in Ordinary Differential Equations (ODE). These two proposed methods are quiteefficient and practically well suited for solving these problems. For us to obtain and verify the accuracy of thenumerical outcomes, we compared the approximate solutions with the exact solution. We found out that there isgood agreement between the exact and approximate solutions. We also compared the performance and thecomputational effort of the two methods. In addition, to achieve more accuracy in the solutions, the step sizeneeds to be very small. Lastly, the error terms have been analyzed for these two methods for different steps sizesand compared also by appropriate examples to demonstrate the reliability and efficiency.