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Basic Ideas of the Homotopy Analysis Method

In: Homotopy Analysis Method in Nonlinear Differential Equations

Author

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  • Shijun Liao

    (Shanghai Jiao Tong University)

Abstract

The basic ideas and all fundamental concepts of the homotopy analysis method (HAM) are described in details by means of two simple examples, including the concept of the homotopy, the flexibility of constructing equations for continuous variations, the way to guarantee convergence of solution series, the essence of the convergence-control parameter c 0, the methods to accelerate convergence, and so on. The corresponding Mathematica codes are given in appendixes and free available online. Beginners of the HAM are strongly suggested to read it first.

Suggested Citation

  • Shijun Liao, 2012. "Basic Ideas of the Homotopy Analysis Method," Springer Books, in: Homotopy Analysis Method in Nonlinear Differential Equations, chapter 0, pages 15-94, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25132-0_2
    DOI: 10.1007/978-3-642-25132-0_2
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