Rational biparameter homotopy perturbation method and Laplace-Padé coupled version
type: Item
instance of: scholarly article
title: Rational biparameter homotopy perturbation method and Laplace-Padé coupled version
zbMATH Open document ID: 1268.65094
DOI: 10.1155/2012/923975
author: H. Vázquez-Leal
author: A. Sarmiento-Reyes
author: Y. Khan
author: A. Díaz-Sanchez
author: U. Filobello-Nino
published in: Journal of Applied Mathematics
publication date: 2013-06-03T00:00:00Z
review text: Summary: 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 Riccati 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.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 6170010
zbMATH Keywords: numerical examples
zbMATH Keywords: rational biparameter homotopy perturbation method
zbMATH Keywords: truncated power series
zbMATH Keywords: nonlinear differential equation
zbMATH Keywords: Van der Pol oscillator
MaRDI profile type: Publication
Wikidata QID: Q58906940
full work available at URL: https://doi.org/10.1155/2012/923975
OpenAlex ID: W2085262331
cites work: Study of convergence of homotopy perturbation method for systems of partial differential equations
cites work: Convergence of the homotopy perturbation method for partial differential equations
cites work: An analytical study for Fisher type equations by using homotopy perturbation method
cites work: He's homotopy perturbation method for solving heat-like and wave-like equations with variable coefficients
cites work: Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method
cites work: Rational homotopy perturbation method
cites work: Application of homotopy perturbation method and variational iteration method to nonlinear oscillator differential equations
cites work: Comparison of homotopy perturbation method and homotopy analysis method
cites work: An elementary introduction to the homotopy perturbation method
cites work: Homotopy perturbation technique
cites work: The homotopy perturbation method for nonlinear oscillators with discontinuities.
cites work: Homotopy perturbation method: a new nonlinear analytical technique
cites work: A coupling method of a homotopy technique and a perturbation technique for nonlinear problems
cites work: Application of homotopy perturbation method to nonlinear wave equations
cites work: Homotopy perturbation method for solving boundary value problems
cites work: A new homotopy perturbation method for solving systems of partial differential equations
cites work: Variational iteration method and homotopy perturbation method for nonlinear evolution equations
cites work: Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations
cites work: The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer
cites work: Solution of the epidemic model by homotopy perturbation method
cites work: The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet
cites work: On the coupling of the homotopy perturbation method and Laplace transformation
cites work: The combined Laplace transform and new homotopy perturbation methods for stiff systems of ODEs
cites work: A homotopy perturbation technique for solving partial differential equations of fractional order in finite domains
cites work: An auxiliary parameter method using Adomian polynomials and Laplace transformation for nonlinear differential equations
cites work: Removal of noise oscillation term appearing in the nonlinear equation solution
cites work: Modified HPMs inspired by homotopy continuation methods
cites work: Application of the homotopy perturbation method to Zakharov-Kuznetsov equations
cites work: Homotopy perturbation method for solving hyperbolic partial differential equations
cites work: Exact solutions for non-linear Schrödinger equations by He's homotopy perturbation method
cites work: He's homotopy perturbation method for systems of integro-differential equations
cites work: Application of homotopy perturbation method for systems of Volterra integral equations of the first kind
cites work: He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind
cites work: Numerical solution for special nonlinear Fredholm integral equation by HPM
cites work: Q4919039
cites work: An aftertreatment technique for improving the accuracy of Adomian's decomposition method
cites work: Solving Riccati differential equation using Adomian's decomposition method
cites work: A new algorithm for the decomposition solution of nonlinear differential equations
cites work: AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING
cites work: On the numerical solution of the model for HIV infection of \(CD4^{+}\) T cells
cites work: Q4076249
cites work: Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method
cites work: The modified homotopy perturbation method for solving strongly nonlinear oscillators
cites work: A comparative study of numerical methods for solving an integro-differential equation
cites work: Solutions of nonlinear oscillators by the modified differential transform method
cites work: An approximate analytic solution of the nonlinear Riccati differential equation
cites work: A reliable aftertreatment for improving the differential transformation method and its application to nonlinear oscillators with fractional nonlinearities
cites work: Interpolants for Runge-Kutta formulas
cites work: Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
cites work: A homotopy approach for nonlinear control synthesis
cites work: Computing equilibria in stochastic finance economies
cites work: A fixed-point homotopy method for solving modified nodal equations
cites work: Threading Homotopies and DC Operating Points of Nonlinear Circuits
cites work: Constructive homotopy methods for finding all or multiple DC operating points of nonlinear circuits and systems

Rational biparameter homotopy perturbation method and Laplace-Padé coupled version (cites work)
cites work: A method for automatically finding multiple operating points in nonlinear circuits

Rational biparameter homotopy perturbation method and Laplace-Padé coupled version (cites work)
cites work: A switching‐parameter algorithm for finding multiple solutions of nonlinear resistive circuits

Rational biparameter homotopy perturbation method and Laplace-Padé coupled version (cites work)
cites work: Variable dimension algorithms for solving resistive circuits

Rational biparameter homotopy perturbation method and Laplace-Padé coupled version (cites work)
cites work: Variable dimension algorithms: Basic theory, interpretations and extensions of some existing methods

Rational biparameter homotopy perturbation method and Laplace-Padé coupled version (cites work)
cites work: A variable dimension fixed point algorithm and the orientation of simplices

Rational biparameter homotopy perturbation method and Laplace-Padé coupled version (DBLP publication ID)
DBLP publication ID: journals/jam/Vazquez-LealSKFD12