Homotopy analysis method: Difference between revisions

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The '''homotopy analysis method (HAM)''' aims to solve [[nonlinear]] [[ordinary differential equation]]s and [[partial differential equation]]s analytically. The method distinguishes itself from other [[Mathematical analysis|analytical methods]] in the following four aspects. First, it is a [[series (mathematics)|series]] expansion method but it is independent of small physical parameters at all. Thus it is applicable for not only weakly but also strongly nonlinear problems. Secondly, the HAM is a unified method for the [[Aleksandr Lyapunov|Lyapunov]] [[artificial small parameter method]], the [[delta expansion method]] and the [[Adomian decomposition method]]. Thirdly, the HAM provides a simple way to ensure the [[Convergence (mathematics)|convergence]] of the solution; also it provides freedom to choose the [[basis function|base function]] of the desired solution. Fourthly, the HAM can be combined with many other [[mathematics|mathematical]] methods—such as [[numerical method]]s, series expansion methods, [[integral transform]] methods and so forth.

The method was devised by Shi-Jun Liao in 1992.[http://numericaltank.sjtu.edu.cn/]