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Homotopy Perturbation Method with an Auxiliary Term

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  • Ji-Huan He

Abstract

The two most important steps in application of the homotopy perturbation method are to construct a suitable homotopy equation and to choose a suitable initial guess. The homotopy equation should be such constructed that when the homotopy parameter is zero, it can approximately describe the solution property, and the initial solution can be chosen with an unknown parameter, which is determined after one or two iterations. This paper suggests an alternative approach to construction of the homotopy equation with an auxiliary term; Dufing equation is used as an example to illustrate the solution procedure.

Suggested Citation

  • Ji-Huan He, 2012. "Homotopy Perturbation Method with an Auxiliary Term," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-7, February.
    • Handle: RePEc:hin:jnlaaa:857612
    DOI: 10.1155/2012/857612
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    Cited by:

    1. 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.
    2. Khudair, Ayad R. & Haddad, S.A.M. & khalaf, Sanaa L., 2017. "Restricted fractional differential transform for solving irrational order fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 81-85.
    3. Zhang, Xiao & Yang, Chunxiao & Yang, Jinge, 2020. "Fast diffusion in a porous building material with a nonlocal source," Applied Mathematics and Computation, Elsevier, vol. 382(C).

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