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Rational Biparameter Homotopy Perturbation Method and Laplace-Padé Coupled Version
Librado Arturo Sarmiento Reyes
ALEJANDRO DIAZ SANCHEZ
Acceso Abierto
Atribución-NoComercial-SinDerivadas
Nonlinear differential equations
Biparameter homotopy
Laplace-Padé
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.
Journal of Applied Mathematics
2012
Artículo
Inglés
Estudiantes
Investigadores
Público en general
Vazquez-Leal, Hector, et al., (2012), Rational Biparameter Homotopy Perturbation Method and Laplace-Padé Coupled Version, Journal of Applied Mathematics, Vol.2012:1-22
ELECTRÓNICA
Versión aceptada
acceptedVersion - Versión aceptada
Appears in Collections:Artículos de Electrónica

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