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2012 Rational Homotopy Perturbation Method
Héctor Vázquez-Leal
J. Appl. Math. 2012: 1-14 (2012). DOI: 10.1155/2012/490342

Abstract

The solution methods of nonlinear differential equations are very important because most of the physical phenomena are modelled by using such kind of equations. Therefore, this work presents a rational version of homotopy perturbation method (RHPM) as a novel tool with high potential to find approximate solutions for nonlinear differential equations. We present two case studies; for the first example, a comparison between the proposed method and the HPM method is presented; it will show how the RHPM generates highly accurate approximate solutions requiring less iteration, in comparison to results obtained by the HPM method. For the second example, which is a Van der Pol oscillator problem, we compare RHPM, HPM, and VIM, finding out that RHPM method generates the most accurate approximated solution.

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Héctor Vázquez-Leal. "Rational Homotopy Perturbation Method." J. Appl. Math. 2012 1 - 14, 2012. https://doi.org/10.1155/2012/490342

Information

Published: 2012
First available in Project Euclid: 2 January 2013

zbMATH: 1251.65119
MathSciNet: MR2979413
Digital Object Identifier: 10.1155/2012/490342

Rights: Copyright © 2012 Hindawi

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