Accuracy of Numerical Methods in the Absence of Closed-Form Solutions for First Order ODEs

Abstract

Ordinary Differential Equations (ODEs) are essential in modeling various real-world phenomena. Finding the analytical solutions to all ODEs is challenging task. In addition, there are very few closed-form solutions. There is a gap in the analysis of ODEs whose solutions exist analytically but cannot be expressed in terms of elementary functions. Majority of the current studies exclusively compare numerical solutions of ODEs with elementary closed-form solutions. This article deals on solving initial value problems having closed form and lacking closed form solutions and compare their accuracy by using Euler method, Improved Euler and RK-4 method. With the idea from closed form solution, this article focuses on the solution of the differential equations to case when the closed form solution is not available.