Engineering and Applied Science Letter
Vol. 6 (2023), Issue 1, pp. 19 – 25
ISSN: 2617-9709 (Online) 2617-9695 (Print)
DOI: 10.30538/psrp-easl2023.0092

Comparative study of the improved Euler’s method and fadugba-falodun scheme for the solution of second order ordinary differential equation

S.E. Fadugba\(^{1,2,3,*}\), K.J. Adebayo \(^1\), A.A. Adeniji \(^4\) and B.O. Falodun\(^5\)
\(^{1}\) Department of Mathematics, Ekiti State University, 360001, Ado Ekiti, Nigeria.
\(^{2}\) Department of Physical Sciences, Mathematics Programme, Landmark University, Omu-Aran, Nigeria.
\(^{3}\) Landmark University SDG 4: Quality Education Research Group, Omu-Aran, Nigeria.
\(^{4}\) Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, South Africa.
\(^{5}\) Department of Computer Science/Mathematics, College of Natural and Applied Sciences, Novena University, Nigeria.

Copyright © 2023 S.E. Fadugba, K.J. Adebayo, A.A. Adeniji and B.O. Falodun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Received: March 01, 2023 – Accepted: April 05, 2023 – Published: June 30, 2023

Abstract

In this paper, the comparative study of Fadugba-Falodun Scheme (FFS) and the Improved Euler’s Method (IEM) is presented. IEM and FFS have been used successfully for the solution of second order ordinary differential equation. FFS is a numerical method recently proposed by means of an interpolating function involving a transcendental function of exponential type. In order to discuss the efficiency and accuracy of the two methods, an illustrative example has been presented in the context of the Exact Solution (ES) and the absolute relative errors computed at each mesh point of the integration interval under consideration. The numerical results show that there is no significant difference between the FFS and ES, unlike its counterpart IEM. Hence, FFS is a good numerical method for the solution of the second order initial value problem in ordinary differential equations. All calculations have been carried out via MATLAB (R2014a) in double precision.

Keywords:

Fadugba-Falodun scheme; Improved Euler method; Initial value problem; Second order ordinary differential equation.