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The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators

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  • D. V. Hieu
  • N. Q. Hai
  • D. T. Hung

Abstract

The Equivalent Linearization Method (ELM) with a weighted averaging is applied to analyze five undamped oscillator systems with nonlinearities. The results obtained via this method are compared with the ones achieved by Parameterized Perturbation Method (PPM), Min–Max Approach (MMA), Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Energy Balance Method (EBM), Harmonic Balance Method (HBM), 4th‐Order Runge‐Kutta Method, and the exact ones. The obtained results demonstrate that this method is very convenient for solving nonlinear equations and also can be successfully applied to a lot of practical engineering and physical problems.

Suggested Citation

  • D. V. Hieu & N. Q. Hai & D. T. Hung, 2018. "The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnljam:v:2018:y:2018:i:1:n:7487851
    DOI: 10.1155/2018/7487851
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    References listed on IDEAS

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    1. Kaya, M.O. & Altay Demirbağ, S., 2009. "Application of parameter expansion method to the generalized nonlinear discontinuity equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1967-1973.
    2. Öziş, Turgut & Yıldırım, Ahmet, 2007. "A note on He’s homotopy perturbation method for van der Pol oscillator with very strong nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 989-991.
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