Content deleted Content added
No edit summary |
No edit summary |
||
Line 1:
{{Primary sources|date=June 2009}}
{{Multiple issues|pov-check=February 2010|COI =August 2010|no footnotes = February 2010}}
{{Infobox scientist
| name = Shing-Tung Yau
| image = [[File:HAM_V2.jpg]]
| caption = Shing-Tung Yau at [[Harvard Law School]] dining hall
| birth_date = {{Birth date and age|1949|04|04}}
| birth_place = [[Shantou]], [[Guangdong Province]], China
| death_date =
| death_place =
| residence = [[United States|U.S.]]
| nationality = [[United States|American]]
| field = [[Mathematics]]
| work_institution = [[Harvard University]], <br /> [[Chinese University of Hong Kong]] <br/>
[[University of Macau]], <br /> [[Zhejiang University]]
| alma_mater = [[Chinese University of Hong Kong]] (B.A. 1969)<br/>[[University of California, Berkeley]] (Ph. D 1971)
| doctoral_advisor = [[Shiing-Shen Chern]]
| doctoral_students = [[Richard Schoen]] (Stanford, 1977)<br>[[Jun Li]] (Stanford, 1989)<br>[[Huai-Dong Cao]] (Princeton, 1986)<br>[[Gang Tian]] (Harvard, 1988)<br>[[Lizhen Ji]] (Northeastern, 1991)<br>[[Kefeng Liu]] (Harvard, 1993)
| known_for =
| prizes = [[Veblen Prize]] (1981)<br>[[Fields Medal]] (1982)<br>[[Crafoord Prize]] (1994)<br>[[National Medal of Science]] (1997)<br>[[Wolf Prize]] (2010)
| religion =
| footnotes =
}}
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 [[limit of a sequence|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.
| |||