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Homotopy perturbation method with rank upgrading technique for the superior nonlinear oscillation

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  • El-Dib, Yusry O.

Abstract

In the present work, the rank upgrade method is suggested to obtain a periodic approximate solution for some complicated nonlinear problems. The method depends on obtaining an equivalent simple equation having a polynomial of nonlinearity without using the Taylor expansion. The solution process is extremely simple, as simple as that by the traditional perturbation method. This approach yields a highly accurate in obtaining analyticity approximate solution for the superior nonlinear oscillation. The results are attractive and valid for both weakly and strongly nonlinear cases.

Suggested Citation

  • El-Dib, Yusry O., 2021. "Homotopy perturbation method with rank upgrading technique for the superior nonlinear oscillation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 555-565.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:555-565
    DOI: 10.1016/j.matcom.2020.11.019
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    References listed on IDEAS

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    1. Ji-Huan He, 2012. "Homotopy Perturbation Method with an Auxiliary Term," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-7, February.
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    Cited by:

    1. El-Dib, Yusry O., 2022. "The damping Helmholtz–Rayleigh–Duffing oscillator with the non-perturbative approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 552-562.

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