Journal of Applied Mathematics

Rational Homotopy Perturbation Method

Héctor Vázquez-Leal

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357153500

Digital Object Identifier
doi:10.1155/2012/490342

Mathematical Reviews number (MathSciNet)
MR2979413

Zentralblatt MATH identifier
1251.65119

Citation

Vázquez-Leal, Héctor. Rational Homotopy Perturbation Method. J. Appl. Math. 2012 (2012), Article ID 490342, 14 pages. doi:10.1155/2012/490342. https://projecteuclid.org/euclid.jam/1357153500


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