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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].
== Frequency Response Analysis for Nonlinear Oscillators ==
The HAM has recently been reported to be useful for obtaining analytical solutions for nonlinear frequency response equations. Such solutions are able to capture various nonlinear behaviors such as hardening-type, softening-type or mixed behaviors of the oscillator<ref>{{cite journal|last1=Tajaddodianfar|first1=Farid|title=Nonlinear dynamics of MEMS/NEMS resonators: analytical solution by the homotopy analysis method|journal=Microsystem Technologies|doi=10.1007/s00542-016-2947-7|url=http://link.springer.com/article/10.1007/s00542-016-2947-7}}</ref>. These analytical equations are also useful in prediction of chaos in nonlinear systems.
== References ==
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