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Variational approach for nonlinear oscillators

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  • He, Ji-Huan

Abstract

We propose a novel variational approach for limit cycles of a kind of nonlinear oscillators. Some examples are given to illustrate the effectiveness and convenience of the method. The obtained results are valid for the whole solution domain with high accuracy.

Suggested Citation

  • He, Ji-Huan, 2007. "Variational approach for nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1430-1439.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:5:p:1430-1439
    DOI: 10.1016/j.chaos.2006.10.026
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    References listed on IDEAS

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    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Construction of solitary solution and compacton-like solution by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 108-113.
    2. Wu, Yue, 2007. "Variational approach to higher-order water-wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 195-198.
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    Cited by:

    1. Park, Inseok & Amarchinta, Hemanth K. & Grandhi, Ramana V., 2010. "A Bayesian approach for quantification of model uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 95(7), pages 777-785.
    2. Tao, Zhao-Ling, 2009. "Frequency–amplitude relationship of nonlinear oscillators by He’s parameter-expanding method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 642-645.
    3. Ali, A.H.A. & Raslan, K.R., 2009. "Variational iteration method for solving partial differential equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1520-1529.
    4. Wang, S. & Wiercigroch, M., 2009. "Forced oscillators with non-linear spring: A simple analytical approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1784-1790.
    5. Zeng, De-Qiang, 2009. "Nonlinear oscillator with discontinuity by the max–min approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2885-2889.
    6. Riley, Matthew E., 2015. "Evidence-based quantification of uncertainties induced via simulation-based modeling," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 79-86.
    7. Allan, Fathi M., 2009. "Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1744-1752.

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