Journal of Applied Mathematics

Rational Homotopy Perturbation Method

Héctor Vázquez-Leal

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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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J. Appl. Math., Volume 2012 (2012), Article ID 490342, 14 pages.

First available in Project Euclid: 2 January 2013

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Vázquez-Leal, Héctor. Rational Homotopy Perturbation Method. J. Appl. Math. 2012 (2012), Article ID 490342, 14 pages. doi:10.1155/2012/490342.

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