Numerical Simulation of Ordinary Differential Equation by Euler and Runge–Kutta Technique

Abstract

In this paper, we explore Modified Euler’s technique & classical Runge Kutta technique of order 4th. These numerical techniques are employed to provide an approximate solution to an initial value problem with ordinary differential equations. These approaches are certainly effective and practically good for solving ordinary differential equations, & they are all used to evaluate degree of accuracy of each approach. We create a table of approximate solution and exact solution comparisons to acquire and assess the level of accuracy of numerical data. The exact and approximate solutions show good agreement, and we compare the computational effort required by the proposed methods. Additionally, we observed that numerical solutions with very short step sizes provide more accurate results. We now identify the errors in the suggested methods and graphically illustrate them to demonstrate their superiority over one another. The Runge-Kutta 4th order approach is more effective in terms of results and also produces less error.