Mathematica Package BVPh

Abstract

The BVPh (version 1.0) is a Mathematica package for highly nonlinear boundary-value/eigenvalue problems with singularity and/or multipoint boundary conditions. It is a combination of the homotopy analysis method (HAM) and the computer algebra system Mathematica, and provides us a convenient analytic tool to solve many nonlinear ordinary differential equations (ODEs) and even some non-linear partial differential equations (PDEs). In this chapter, we briefly describe its scope, the basic mathematical formulas, and the choice of base functions, initial guess and the auxiliary linear operator, and so on, together with a simple users guide. As open resource, the BVPh 1.0 is given in the appendix of this chapter and free available (Accessed 25 Nov 2011, will be updated in the future) at