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 nonlinear 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 http://numericaltank.sjtu.edu.cn/BVPh.htm

Keywords

Initial Guess Computer Algebra System Linear Differential Operator Chebyshev Series Auxiliary Linear Operator 
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Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shijun Liao
    • 1
  1. 1.Shanghai Jiao Tong UniversityShanghaiChina

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