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Homotopy Analysis Method

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Encyclopedia of Ocean Engineering

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Abstract

In this entry, we describe the basic ideas of the homotopy analysis method (HAM), an analytic approach to get convergent series solutions of strongly nonlinear problems, which recently attracts interests of more and more researchers. HAM fundamentally overcomes the excessive dependence on small parameters in the framework of perturbation theory, and its validity has nothing to do with small/large physical parameter of the studied nonlinear problem. So, it has a wide range of applications. In addition, HAM provides us great freedom to choose the base function, so that a better base function can be selected to approximate the solution of the problem more effectively. Furthermore, unlike all other analytical approximation methods, we can guarantee the convergence of solution series in a simple way in the framework of HAM. In general, HAM provides a new way of thinking that how to get the analytical approximate solution for nonlinear problems and opens up a new way for solving nonlinear problems (especially strong nonlinear problems without small parameters).

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Authors and Affiliations

  1. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, China

    Xiaoyan Yang & Zhiliang Lin

Authors
  1. Xiaoyan Yang
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  2. Zhiliang Lin
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Correspondence to Zhiliang Lin .

Editor information

Editors and Affiliations

  1. Hadal Science and Technology Research Center, Shanghai Ocean University, Shanghai, China

    Weicheng Cui

  2. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, China

    Shixiao Fu

  3. School of Marine Science and Technology, Newcastle University, Newcastle, UK

    Zhiqiang Hu

Section Editor information

  1. Hadal Science and Technology Center, Shanghai Ocean University, Shanghai, Select State/Province, China

    Zhe Jiang

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Yang, X., Lin, Z. (2020). Homotopy Analysis Method. In: Cui, W., Fu, S., Hu, Z. (eds) Encyclopedia of Ocean Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-6963-5_271-1

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  • DOI: https://doi.org/10.1007/978-981-10-6963-5_271-1

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6963-5

  • Online ISBN: 978-981-10-6963-5

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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