Application of He's energy balance method to Duffing-harmonic oscillators

DOI10.1080/00207160903337239zbMath1211.65092OpenAlexW2101742004MaRDI QIDQ5391469

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Publication date: 6 April 2011

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160903337239

zbMATH Keywords

numerical examplesHamiltonianHe's energy balance methodnonlinear Duffing oscillators

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Approximation methods and numerical treatment of dynamical systems (37M99) Oscillation, growth of solutions to ordinary differential equations in the complex domain (34M10) Numerical problems in dynamical systems (65Pxx)

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Cites Work

• A new analytical approximation to the Duffing-harmonic oscillator
• Determination of the frequency-amplitude relation for a Duffing-harmonic oscillator by the energy balance method
• New analytical methods for cleaning up the solution of nonlinear equations
• Application of homotopy perturbation method and variational iteration method to nonlinear oscillator differential equations
• A new analytical approach to the Duffing-harmonic oscillator
• Variational approach for nonlinear oscillators
• MATHEMATICAL AND NUMERICAL STUDY OF THE DUFFING-HARMONIC OSCILLATOR
• Analytical study on a Duffing-harmonic oscillator
• Solution of a Duffing-harmonic oscillator by the method of harmonic balance
• Higher accuracy analytical approximations to the Duffing-harmonic oscillator
• Solutions of the Duffing-harmonic oscillator by an iteration procedure
• The frequency–amplitude relationship for some nonlinear oscillators with discontinuity by He's variational method

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