An improvement to the homotopy perturbation method for solving nonlinear Duffing's equations

DOI10.1007/s40840-015-0191-4zbMath1448.65066OpenAlexW2215502576MaRDI QIDQ1746735

A. R. Vahidi, Z. Azimzadeh, Esmail Babolian

Publication date: 25 April 2018

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40840-015-0191-4

zbMATH Keywords

Padé approximanthomotopy perturbation methodnonlinear Duffing's equations

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Padé approximation (41A21) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items

Existence of solution of functional Volterra-Fredholm integral equations in space \(L^\infty(\mathbb{R}_+)\) and sinc interpolation to find solution ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homotopy perturbation method for nonlinear partial differential equations of fractional order
• Solutions of a class of singular second-order IVPs by homotopy-perturbation method
• Exact solutions for non-linear Schrödinger equations by He's homotopy perturbation method
• He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind
• Beyond Adomian polynomials: He polynomials
• Application of homotopy-perturbation method to Klein-Gordon and sine-Gordon equations
• Application of homotopy-perturbation method to nonlinear population dynamics models
• An efficient method for quadratic Riccati differential equation
• Variational iteration method -- a kind of non-linear analytical technique: Some examples
• Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations
• Homotopy-perturbation method for pure nonlinear differential equation
• Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations
• Solving frontier problems of physics: the decomposition method
• A simple perturbation approach to Blasius equation
• Integrable Duffing's maps and solutions of the Duffing equation
• An aftertreatment technique for improving the accuracy of Adomian's decomposition method
• A coupling method of a homotopy technique and a perturbation technique for nonlinear problems
• A new analytical approach to the Duffing-harmonic oscillator
• Comparison of homotopy perturbation method and homotopy analysis method
• Viscoelastic MHD flow boundary layer over a stretching surface with viscous and ohmic dissipations
• Homotopy perturbation technique
• The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer
• Homotopy perturbation method for thin film flow of a third-grade fluid down an inclined plane
• Numerical solutions of the integral equations: homotopy perturbation method and Adomian's decomposition method
• Numerical solution of Duffing equation by the Laplace decomposition algorithm
• Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order
• The homotopy-perturbation method applied for solving complex-valued differential equations with strong cubic nonlinearity
• Analysis of velocity equation of steady flow of a viscous incompressible fluid in channel with porous walls
• Exact solution of a difference approximation to Duffing's equation
• Best difference equation approximation to Duffing's equation
• Approximate analytical solution of Blasius' equation

This page was built for publication: An improvement to the homotopy perturbation method for solving nonlinear Duffing's equations