Comparison Between Runge-Kutta Method, Euler Method and Modified Euler Method for Difference Order of Ordinary Differential Equation

Abstract

Ordinary Differential Equations with Initial Value Problems (IVP) are commonly used in almost every section such as in Engineering, Physics, and Mathematics. The problems regarding Differential Equations have arisen a lot in our field area. This research focuses on finding the best method between the three methods which are Euler Method, Modified Euler Method, and Runge-Kutta Method to solve the Ordinary Differential Equation with IVP problems in a different order by reducing to the system of first-order. In this article, the differential equation with first-order, second-order, and third-order were used to determine the accuracy by the three methods. To determine the optimal method, the errors of all three methods are computed and compared to identify which one yields the least errors. The analysis indicates that the Modified Euler method outperforms both the Euler and Runge-Kutta methods in solving Ordinary Differential Equations with differing orders.