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Application of parameter expansion method to the generalized nonlinear discontinuity equation

Author

Listed:
  • Kaya, M.O.
  • Altay Demirbağ, S.

Abstract

In this paper, we introduce the generalized nonlinear discontinuity equation for the first time and solve the problem by using He’s modified Lindstedt–Poincaré method and bookkeeping parameter method known as parameter expansion method. We obtain sufficiently accurate solutions with a first-order approximation that are valid for whole domain. The solutions obtained using the approach presented here are then compared to those in the literature and are found to agree well with them.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:1967-1973
    DOI: 10.1016/j.chaos.2009.03.143
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    References listed on IDEAS

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    1. Beléndez, A. & Beléndez, T. & Márquez, A. & Neipp, C., 2008. "Application of He’s homotopy perturbation method to conservative truly nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 770-780.
    2. Marinca, Vasile & Herişanu, Nicolae, 2008. "Periodic solutions of Duffing equation with strong non-linearity," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 144-149.
    3. Hemeda, A.A., 2009. "Variational iteration method for solving non-linear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1297-1303.
    4. Wang, Shu-Qiang & He, Ji-Huan, 2008. "Nonlinear oscillator with discontinuity by parameter-expansion method," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 688-691.
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    Cited by:

    1. 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).

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