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,]] Mapleor and so on[[Maple]], one can gain analytic approximations of a highly nonlinear problem atto aarbitrarily high enough order by means of the HAM in only a few seconds. ReplacingInspired pencilby the recent successful applications of the HAM in different fields, papera andMathematica traditionalpackage calculatorbased byon keyboardthe HAM, hardcalled diskBVPh, andhas CPUsbeen ofmade available online for solving nonlinear boundary-value problems.[http://numericaltank.sjtu.edu.cn/BVPh.htm] BVPh is a laptopsolver computer,package onefor canhighly easilynonlinear ODEs with readsingularities, calculatemultiple solutions, and savemultipoint analyticboundary resultsconditions obtainedin byeither thea HAMfinite inor onlyan ainfinite fewinterval, secondsand includes support for certain types of nonlinear PDEs. ThusAnother HAM-based Mathematica code, theAPOh, HAMhas isbeen inproduced essenceto solve for an explicit analytic approximation method forof the computeroptimal era.exercise boundary of American put option, which is also available online.[http://numericaltank.sjtu.edu.cn/APO.htm]
Inspirited by so many successful applications of the HAM in different fields and also by the ability of "computing with functions instead of numbers" of computer algebra systems such as [[Mathematica]], [[Matlab]], and [[Maple]], a Mathematica package based on the HAM, called BVPh, was issued for solving nonlinear boundary-value problems. It is available online.[http://numericaltank.sjtu.edu.cn/BVPh.htm] The HAM-based Mathematica package 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 even for some types of nonlinear PDEs. Another HAM-based Mathematica code APOh has been produced to solve for an explicit analytic approximations of the optimal exercise boundary of American put option, which is also available online.[http://numericaltank.sjtu.edu.cn/APO.htm]
