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The '''homotopy analysis method''' ('''HAM''') is a semi-analytical technique to solve [[nonlinear]] [[ordinary differential equations|ordinary]]/[[partial differential equations|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-[[Taylor series|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<ref>{{citation | last=Liao | first=S.J. | title=The proposed homotopy analysis technique for the solution of nonlinear problems | publisher=PhD thesis, Shanghai Jiao Tong University | year=1992 }}</ref> and further modified<ref>{{citation | last=Liao | first=S.J. | title=An explicit, totally analytic approximation of Blasius’ viscous flow problems | journal=International Journal of Non-Linear Mechanics | volume=34 | issue=4 | pages=759–778 | year=1999 | doi=10.1016/S0020-7462(98)00056-0|bibcode = 1999IJNLM..34..759L }}</ref> in 1997 to
== Characteristics==
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