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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
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><ref>{{cite journal|last1=Tajaddodianfar|first1=Farid|title=On the dynamics of bistable micro/nano resonators: Analytical solution and nonlinear behavior|journal=Communications in Nonlinear Science and Numerical Simulation|volume=20|issue=3|doi=10.1016/j.cnsns.2014.06.048|url=http://www.sciencedirect.com/science/article/pii/S1007570414003116}}</ref> These analytical equations are also useful in prediction of chaos in nonlinear systems.<ref>{{cite journal|last1=Tajaddodianfar|first1=Farid|title=Prediction of chaos in electrostatically actuated arch micro-nano resonators: Analytical approach|journal=Communications in Nonlinear Science and Numerical Simulation|volume=30|doi=10.1016/j.cnsns.2015.06.013|url=http://www.sciencedirect.com/science/article/pii/S1007570415002142}}</ref>
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