Homotopy analysis method

The homotopy analysis method (HAM) is a semi-analytical technique to solve <a href="/facts/Nonlinear/4aYItALC">nonlinear</a> <a href="/facts/Ordinary_differential_equations/ygKGQ8kD">ordinary</a>/<a href="/facts/Partial_differential_equations/DyPsBlv7">partial</a> <a href="/facts/Differential_equations/9MGbE3Ca">differential equations</a>. The homotopy analysis method employs the concept of the <a href="/facts/Homotopy/1nWrPxdj">homotopy</a> from <a href="/facts/Topology/2EqW47cU">topology</a> to generate a convergent series solution for nonlinear systems. This is enabled by utilizing a homotopy-<a href="/facts/Taylor_series/M0aTuftH">Maclaurin series</a> to deal with the nonlinearities in the system.
The HAM was first devised in 1992 by <a href="/facts/Liao_Shijun/ypRD5uw4">Liao Shijun</a> of <a href="/facts/Shanghai_Jiaotong_University/5cFSHwyt">Shanghai Jiaotong University</a> in his PhD dissertation and further modified in 1997 to introduce a non-zero auxiliary parameter, referred to as the convergence-control parameter, c0, to construct a homotopy on a differential system in general form. The convergence-control parameter is a non-physical variable that provides a simple way to verify and enforce convergence of a solution series. The capability of the HAM to naturally show convergence of the series solution is unusual in analytical and semi-analytic approaches to nonlinear partial differential equations.

Homotopy analysis method open-in-new

Homotopy analysis method