Journal of Applied Mathematics · 2012 · 32 citations · 9 references
Natural SciencesPhysicsComputational MechanicsComputational PhysicsDifferential EquationsNonlinear DynamicsNumerical Methods For Differential EquationsOscillatorsDuffing OscillatorNonlinear OscillationsNonlinear Oscillator AnalysisNonlinear OscillatorsOscillator ModelingOscillator NonlinearityOscillator TheoryPeriodic Solutions Of Differential Equations
Energy balance method (EBM) is extended for high‐order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic‐quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first‐ and second‐order approximation, respectively. The third‐order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator.
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Hassan Askari, Zia Saadatnia, M. Kalami-Yazdi et al. · Computers & Mathematics with Applications · 2011 · 41 citations