Homotopy analysis method: Difference between revisions

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== The HAM and computer algebra ==

The HAM is an analytic approximation method designed for the computer era with the goal of "computing with functions instead of numbers." In conjunction with a computer algebra system such as [[Mathematica]] or [[Maple]], one can gain analytic approximations of a highly nonlinear problem to arbitrarily high order by means of the HAM in only a few seconds. Inspired by the recent successful applications of the HAM in different fields, a Mathematica package based on the HAM, called BVPh, has been made available online for solving nonlinear boundary-value problems. [http://numericaltank.sjtu.edu.cn/BVPh.htm]. BVPh is a solver package for highly nonlinear ODEs with singularities, multiple solutions, and multipoint boundary conditions in either a finite or an infinite interval, and includes support for certain types of nonlinear PDEs.<ref name="HAM in NDEs"/> Another HAM-based Mathematica code, APOh, has been produced to solve for an explicit analytic approximation of the optimal exercise boundary of American put option, which is also available online. [http://numericaltank.sjtu.edu.cn/APO.htm].

== References ==