The multi-parameter homotopy harmonic balance method for steady state problems
DOI10.1080/00207160903229899zbMath1191.65086OpenAlexW2027897501MaRDI QIDQ3568475
Andrew Y. T. Leung, T. C. Fung, Zhongjin Guo
Publication date: 11 June 2010
Published in: International Journal of Computer Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00207160903229899
chaoshomotopy continuationnumerical examplessteady state solutionsDuffing equationmultiple bifurcationsperiod doublingnonlinear vibration problemmulti-parameter homotopy harmonic balance method
Nonlinear ordinary differential equations and systems (34A34) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Bifurcations of singular points in dynamical systems (37G10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical chaos (65P20) Numerical bifurcation problems (65P30)
Cites Work
- Comparison between Adomian's method and He's homotopy perturbation method
- Galerkin's procedure for nonlinear periodic systems
- Numerical computation of nonlinear forced oscillations by Galerkin's procedure
- On the transition from regular to chaotic behaviour in the Duffing oscillator
- Bounds on the Fourier coefficients for the periodic solutions of non-linear oscillator equations
- Harmonic balance calculations by using matrices
- Construction of chaotic regions
- Amplitude Incremental Variational Principle for Nonlinear Vibration of Elastic Systems
- On the Structure of Jacobians for Spectral Methods for Nonlinear Partial Differential Equations
- Efficient numerical treatment of periodic systems with application to stability problems
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