Engineering and Applied Science Letter
Vol. 7 (2024), Issue 1, pp. 1 – 8
ISSN: 2617-9709 (Online) 2617-9695 (Print)
DOI: 10.30538/psrp-easl2024.0095
Exploring effective iterative methods for nonlinear equations by using variational iteration technique
Farooq Ahmed Shah\(^{1,*}\) and Muhammad Aslam Noor\(^2\)
\(^{1}\) Department of Mathematics, COMSATS University Islamabad, Attock Campus Pakistan
\(^{2}\) Department of Mathematics, COMSATS University Islamabad, Pakistan
Copyright © 2024 Farooq Ahmed Shah and Muhammad Aslam Noor. 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: May 06, 2023 – Accepted: February 20, 2024 – Published: March 31, 2024
Abstract
The purpose of this paper is to introduce and evaluate novel iterative methods for approximating solutions to nonlinear equations, which leverage the power of the variational iteration technique. Specifically, we present a comprehensive analysis of the proposed methods and demonstrate their effectiveness through various examples. Moreover, we provide a comparative analysis with other existing methods and conclude that the newly developed methods offer a competitive alternative. Our results highlight the potential of this approach in generating a diverse set of iterative methods for solving nonlinear equations. Therefore, this study contributes to the ongoing efforts to improve the efficiency and accuracy of nonlinear equation solving techniques.
Keywords:
Nonlinear equations; Iterative method; Convergence; Newton’s method; Taylor series; Examples