Open Access
Translator Disclaimer
2012 Rational Biparameter Homotopy Perturbation Method and Laplace-Padé Coupled Version
Hector Vazquez-Leal, Arturo Sarmiento-Reyes, Yasir Khan, Uriel Filobello-Nino, Alejandro Diaz-Sanchez
J. Appl. Math. 2012: 1-21 (2012). DOI: 10.1155/2012/923975


The fact that most of the physical phenomena are modelled by nonlinear differential equations underlines the importance of having reliable methods for solving them. This work presents the rational biparameter homotopy perturbation method (RBHPM) as a novel tool with the potential to find approximate solutions for nonlinear differential equations. The method generates the solutions in the form of a quotient of two power series of different homotopy parameters. Besides, in order to improve accuracy, we propose the Laplace-Padé rational biparameter homotopy perturbation method (LPRBHPM), when the solution is expressed as the quotient of two truncated power series. The usage of the method is illustrated with two case studies. On one side, a Ricatti nonlinear differential equation is solved and a comparison with the homotopy perturbation method (HPM) is presented. On the other side, a nonforced Van der Pol Oscillator is analysed and we compare results obtained with RBHPM, LPRBHPM, and HPM in order to conclude that the LPRBHPM and RBHPM methods generate the most accurate approximated solutions.


Download Citation

Hector Vazquez-Leal. Arturo Sarmiento-Reyes. Yasir Khan. Uriel Filobello-Nino. Alejandro Diaz-Sanchez. "Rational Biparameter Homotopy Perturbation Method and Laplace-Padé Coupled Version." J. Appl. Math. 2012 1 - 21, 2012.


Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1268.65094
MathSciNet: MR3000278
Digital Object Identifier: 10.1155/2012/923975

Rights: Copyright © 2012 Hindawi


Vol.2012 • 2012
Back to Top