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Basic Ideas of the Homotopy Analysis Method

  • Shijun Liao

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.

Keywords

Computer Algebra System Auxiliary Parameter Stable Equilibrium Point Deformation Equation Iteration Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shijun Liao
    • 1
  1. 1.Shanghai Jiao Tong UniversityShanghaiChina

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