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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 490342, 14 pages
Research Article

Rational Homotopy Perturbation Method

Electronic Instrumentation and Atmospheric Sciences School, University of Veracruz, Circuito Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, VER, Mexico

Received 28 June 2012; Accepted 16 August 2012

Academic Editor: Turgut Öziş

Copyright © 2012 Héctor Vázquez-Leal. 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.


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.