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Homotopy perturbation method for strongly nonlinear oscillators

Author

Listed:
  • He, Ji-Huan
  • Jiao, Man-Li
  • Gepreel, Khaled A.
  • Khan, Yasir

Abstract

This paper reveals the effectiveness of the homotopy perturbation method for strongly nonlinear oscillators. A generalized Duffing oscillator is adopted to elucidate the solving process step by step, and a nonlinear frequency–amplitude relationship is obtained with a relative error of 0.91% when the amplitude tends to infinity, the solution morphology is also discussed, and the zero-th approximate solution is enough for conservative nonlinear oscillators, while the accuracy of the frequency can be improved if the iteration continues.

Suggested Citation

  • He, Ji-Huan & Jiao, Man-Li & Gepreel, Khaled A. & Khan, Yasir, 2023. "Homotopy perturbation method for strongly nonlinear oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 243-258.
    • Handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:243-258
    DOI: 10.1016/j.matcom.2022.08.005
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    References listed on IDEAS

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    1. Ghaleb, A.F. & Abou-Dina, M.S. & Moatimid, G.M. & Zekry, M.H., 2021. "Analytic approximate solutions of the cubic–quintic Duffing–van​ der Pol equation with two-external periodic forcing terms: Stability analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 129-151.
    2. Che Han & Yu-Lan Wang & Zhi-Yuan Li, 2021. "NUMERICAL SOLUTIONS OF SPACE FRACTIONAL VARIABLE-COEFFICIENT KdV–MODIFIED KdV EQUATION BY FOURIER SPECTRAL METHOD," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-19, December.
    3. Dan Tian & Qura-Tul Ain & Naveed Anjum & Chun-Hui He & Bin Cheng, 2021. "Fractal N/Mems: From Pull-In Instability To Pull-In Stability," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(02), pages 1-8, March.
    4. Chun-Hui He & Chao Liu, 2022. "A Modified Frequency–Amplitude Formulation For Fractal Vibration Systems," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-8, May.
    5. Muhammad Suleman & Qingbiao Wu, 2015. "Comparative Solution of Nonlinear Quintic Cubic Oscillator Using Modified Homotopy Perturbation Method," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-5, June.
    6. Zhou, Liangqiang & Chen, Fangqi, 2022. "Chaos of the Rayleigh–Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 1-18.
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    Cited by:

    1. Remus-Daniel Ene & Nicolina Pop, 2023. "Optimal Homotopy Asymptotic Method for an Anharmonic Oscillator: Application to the Chen System," Mathematics, MDPI, vol. 11(5), pages 1-14, February.
    2. Shirazian, Mohammad, 2023. "A new acceleration of variational iteration method for initial value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 246-259.
    3. Alim, Md. Abdul & Kawser, M. Abul, 2023. "Illustration of the homotopy perturbation method to the modified nonlinear single degree of freedom system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

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