Applied Mathematics and Mechanics

, Volume 19, Issue 10, pp 957–962 | Cite as

Homotopy analysis method: A new analytic method for nonlinear problems

  • Liao Shijun


In this paper, the basic ideas of a new analytic technique, namely the Homotopy Analysis Method (HAM), are described. Different from perturbation methods, the validity of the HAM is independent on whether or not there exist small parameters in considered nonlinear equations. Therefore, it provides us with a powerful analytic tool for strongly nonlinear problems. A typical nonlinear problem is used as an example to verify the validity and the great potential of the HAM.

Key words

nonlinear analytic technique strong nonlinearity homotopy topology 


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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Liao Shijun
    • 1
  1. 1.Shanghai Jiaotong UniversityShanghaiP. R. China

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