An improvement to the homotopy perturbation method for solving nonlinear Duffing's equations
type: Item
instance of: scholarly article
title: An improvement to the homotopy perturbation method for solving nonlinear Duffing's equations
zbMATH Open document ID: 1448.65066
author: A. R. Vahidi
author: Z. Azimzadeh
author: E. Babolian
published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series
publication date: 2018-04-25T00:00:00Z
review text: A new form of the homotopy perturbation method is developed to solve Duffing's equations. The truncated series solution coincides with the Mandarin expansion of the true solution. In order to obtain a more accurate solution, a Laplace transformation is applied to the truncated Mandarin series and the Padé approximation. This method does not require to calculate He's polynomials. Therefore, the new method is much faster. The numerical results indicated that the method is very efficient and converges to the exact solution of nonlinear Duffing's equations.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 6864671
zbMATH Keywords: homotopy perturbation method
zbMATH Keywords: nonlinear Duffing's equations
zbMATH Keywords: Padé approximant
reviewed by: Bülent Karasözen
MaRDI profile type: Publication
full work available at URL: s40840-015-0191-4
OpenAlex ID: W2215502576
cites work: Numerical solutions of the integral equations: homotopy perturbation method and Adomian's decomposition method
cites work: Solving frontier problems of physics: the decomposition method
cites work: An efficient method for quadratic Riccati differential equation
cites work: Analysis of velocity equation of steady flow of a viscous incompressible fluid in channel with porous walls
cites work: Q3739430
cites work: Exact solutions for non-linear Schrödinger equations by He's homotopy perturbation method
cites work: He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind
cites work: Solutions of a class of singular second-order IVPs by homotopy-perturbation method
cites work: Application of homotopy-perturbation method to nonlinear population dynamics models
cites work: Application of homotopy-perturbation method to Klein-Gordon and sine-Gordon equations
cites work: The homotopy-perturbation method applied for solving complex-valued differential equations with strong cubic nonlinearity
cites work: Homotopy-perturbation method for pure nonlinear differential equation
cites work: The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer
cites work: Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations
cites work: Beyond Adomian polynomials: He polynomials
cites work: Homotopy perturbation technique
cites work: Approximate analytical solution of Blasius' equation
cites work: Variational iteration method -- a kind of non-linear analytical technique: Some examples
cites work: A coupling method of a homotopy technique and a perturbation technique for nonlinear problems
cites work: A simple perturbation approach to Blasius equation
cites work: Comparison of homotopy perturbation method and homotopy analysis method
cites work: An aftertreatment technique for improving the accuracy of Adomian's decomposition method
cites work: Viscoelastic MHD flow boundary layer over a stretching surface with viscous and ohmic dissipations
cites work: A new analytical approach to the Duffing-harmonic oscillator
cites work: Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations
cites work: Homotopy perturbation method for nonlinear partial differential equations of fractional order
cites work: Integrable Duffing's maps and solutions of the Duffing equation
cites work: Perturbation methods.
cites work: Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order
cites work: Best difference equation approximation to Duffing's equation
cites work: Exact solution of a difference approximation to Duffing's equation
cites work: Homotopy perturbation method for thin film flow of a third-grade fluid down an inclined plane
cites work: Restarted Adomian's decomposition method for Duffing's equation
cites work: Numerical solution of Duffing equation by the Laplace decomposition algorithm
DOI: 10.1007/S40840-015-0191-4
description: scientific article; zbMATH DE number 6864671