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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. Muhammad Suleman & Qingbiao Wu, 2015. "Comparative Solution of Nonlinear Quintic Cubic Oscillator Using Modified Homotopy Perturbation Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    2. Abdon Atangana & Dumitru Baleanu, 2013. "Nonlinear Fractional Jaulent‐Miodek and Whitham‐Broer‐Kaup Equations within Sumudu Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. 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.
    5. 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.
    6. Lan Xu & Eric W. M. Lee, 2013. "Variational Iteration Method for the Magnetohydrodynamic Flow over a Nonlinear Stretching Sheet," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Asma Ali Elbeleze & Adem Kiliçman & Bachok M. Taib, 2012. "Application of Homotopy Perturbation and Variational Iteration Methods for Fredholm Integrodifferential Equation of Fractional Order," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. İhsan Timuçin Dolapçı & Mehmet Şenol & Mehmet Pakdemirli, 2013. "New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    9. Hector Vazquez-Leal & Yasir Khan & Uriel Filobello-Nino & Arturo Sarmiento-Reyes & Alejandro Diaz-Sanchez & Luis-F. Cisneros-Sinencio, 2013. "Fixed‐Term Homotopy," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    10. 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).
    11. Y. Y. Lee, 2012. "Analysis of the Nonlinear Structural‐Acoustic Resonant Frequencies of a Rectangular Tube with a Flexible End Using Harmonic Balance and Homotopy Perturbation Methods," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    12. Ali Akgül & Adem Kılıçman & Mustafa Inc, 2013. "Improved (G′/G)‐Expansion Method for the Space and Time Fractional Foam Drainage and KdV Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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