About: Homotopy analysis method

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The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear ordinary/partial differential equations. The homotopy analysis method employs the concept of the homotopy from topology to generate a convergent series solution for nonlinear systems. This is enabled by utilizing a homotopy-Maclaurin series to deal with the nonlinearities in the system.

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rdfs:label	Homotopy analysis method (en)
rdfs:comment	The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear ordinary/partial differential equations. The homotopy analysis method employs the concept of the homotopy from topology to generate a convergent series solution for nonlinear systems. This is enabled by utilizing a homotopy-Maclaurin series to deal with the nonlinearities in the system. (en)
foaf:depiction
dcterms:subject	Asymptotic analysis Homotopy theory Partial differential equations
Wikipage page ID	22844401 (xsd:integer)
Wikipage revision ID	1117735594 (xsd:integer)
Link from a Wikipage to another Wikipage	Basis functions Electrohydrodynamic Limit cycle Limit of a sequence Mathematica Mathematical analysis Gravity waves Boundary element method Liao Shijun Linear operator Perturbation theory Asymptotic analysis Topology Heat transfer Aleksandr Lyapunov Nonlinear Padé approximant Partial differential equation Partial differential equations Numerical continuation Put option Homotopy theory Taylor series Partial differential equations Adomian decomposition method Homotopy Homotopy perturbation method Differential equations Maple (software) Ordinary differential equations Series (mathematics) Stochastic volatility Poisson–Boltzmann equation Navier–Stokes equation Shanghai Jiaotong University Spectral methods Wave resonance
Link from a Wikipage to an external page	http://numericaltank.sjtu.edu.cn/APO.htm http://numericaltank.sjtu.edu.cn/BVPh.htm
sameAs	Homotopy analysis method Homotopy analysis method Homotopy analysis method Homotopy analysis method Homotopy analysis method
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has abstract	The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear ordinary/partial differential equations. The homotopy analysis method employs the concept of the homotopy from topology to generate a convergent series solution for nonlinear systems. This is enabled by utilizing a homotopy-Maclaurin series to deal with the nonlinearities in the system. The HAM was first devised in 1992 by Liao Shijun of Shanghai Jiaotong University 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. (en)
gold:hypernym	Technique
prov:wasDerivedFrom	wikipedia-en:Homotopy_analysis_method?oldid=1117735594&ns=0
page length (characters) of wiki page	16560 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Homotopy_analysis_method
is Link from a Wikipage to another Wikipage of	Duffing equation Index of physics articles (H) Liao Shijun Partial differential equation Ham (disambiguation) Adomian decomposition method Homotopy Homotopy perturbation method Homotopy perturbation technique
is Wikipage redirect of	Homotopy perturbation method Homotopy perturbation technique
is Wikipage disambiguates of	Ham (disambiguation)
is foaf:primaryTopic of	wikipedia-en:Homotopy_analysis_method

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