The iterative homotopy harmonic balance method for conservative Helmholtz-Duffing oscillators

DOI10.1016/j.amc.2009.09.014zbMath1183.65083OpenAlexW2095416790MaRDI QIDQ846405

Zhongjin Guo, Andrew Y. T. Leung

Publication date: 9 February 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.09.014

zbMATH Keywords

periodic solutionsnumerical examplesasymmetric equationconservative Helmholtz-Duffing oscillatorsiterative homotopy harmonic balance methodparameter-expansion technique

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items

Global residue harmonic balance method to periodic solutions of a class of strongly nonlinear oscillators ⋮ Effective approximate methods for strongly nonlinear differential equations with oscillations ⋮ Iterative homotopy harmonic balance approach for determining the periodic solution of a strongly nonlinear oscillator ⋮ Approximate periodic solutions for the Helmholtz-Duffing equation ⋮ A finite extensibility nonlinear oscillator ⋮ Exact solutions for the quadratic mixed-parity Helmholtz-Duffing oscillator by bifurcation theory of dynamical systems ⋮ Multiple-parameter Hamiltonian approach for higher accurate approximations of a nonlinear oscillator with discontinuity ⋮ Solutions of the force-free Duffing-van der Pol oscillator equation

Cites Work

• Application of He's variational iteration method to Helmholtz equation
• Variational iteration method -- a kind of non-linear analytical technique: Some examples
• An analytical approximate technique for a class of strongly non-linear oscillators
• The homotopy perturbation method for nonlinear oscillators with discontinuities.
• A coupling method of a homotopy technique and a perturbation technique for nonlinear problems
• Global optimal control and system-dependent solutions in the hardening Helmholtz--Duffing oscillator
• Homotopy perturbation method: a new nonlinear analytical technique
• Asymptotology by homotopy perturbation method
• Homotopy perturbation technique
• Application of the extended homotopy perturbation method to a kind of nonlinear evolution equations
• Quadratic non-linear oscillators
• Stability transitions of certain exact periodic responses in undamped helmholtz and duffing oscillators
• Solution of a quadratic nonlinear oscillator by the method of harmonic balance
• He's frequency formulation for nonlinear oscillators
• SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS
• Letter to the Editor