Development of Homotopy Perturbation Method for Solving Nonlinear Algebraic Equations

Bachir. N. Kharrat¹ , George. A. Toma²

1. Dept. of Mathematics, Faculty of Sciences, Aleppo University, Aleppo, Syria.
2. Dept. of Mathematics, Faculty of Sciences, Aleppo University, Aleppo, Syria.

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.2 , pp.47-50, Apr-2020

Online published on Apr 30, 2020

Copyright © Bachir. N. Kharrat, George. A. Toma . 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.
 

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Abstract :
In this paper, we proposed expanding the application of the He`s homotopy perturbation method to solve nonlinear algebraic equations using the first seven terms of Taylor`s series. The main objective of our research is to find an approximate solution with high accuracy for solving non-linear algebraic equations. In the proposed hybrid scheme, we combined the homotopy perturbation method with the Taylor`s series for an analytical function, by truncating the first seven terms of Taylor`s series and then apply the homotopy perturbation method. We demonstrated the efficacy of the proposed method by finding an approximate solution with high accuracy. This solution is the intersection of the graph with the horizontal axis. We also found a new iterative formula that gives, in every iteration, an approximate solution that converges from the exact solution faster and with small error. Numerical examples are given to show the efficiency and accuracy of the proposed iterative scheme.

Key-Words / Index Term :
Homotopy Perturbation Method, Iterative Scheme, Nonlinear Algebraic Equations, Taylor`s Series

References :
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