**Mathematica
package BVPh 1.0**

**A Simple Users Guide Copyright Statement Examples ****Publications**

Inspirited by the general validity of the homotopy
analysis method (HAM) in so many different fields and by the ability of
“computing with functions instead of numbers” provided by computer algebra
system such as Mathematica and Maple, a HAM-based Mathematica package **BVPh** (version 1.0) is developed for
highly nonlinear boundary-value/eigenvalue equations. The **BVPh
1.0** is mainly valid for nonlinear ordinary differential equation with
singularity, multiple solutions and/or multi-point boundary conditions in a
finite or an infinite interval. It
is even valid for some nonlinear partial differential equations related to
boundary-layer flows. The aim is to
develop a kind of analytic tool for as **many**
nonlinear boundary-value problems (BVPs) as **possible** such that multiple solutions of some highly nonlinear BVPs
can be conveniently found out, and that the infinite interval and singularity
of governing equations and/or multi-point boundary conditions can be easily
resolved.

Twelve examples for the use of the **BVPh 1.0** are given in Part II of the
book:

Liao, S.J.: **Homotopy
Analysis Method in Nonlinear Differential Equations**. Higher
Education Press & Springer, Beijing and Heidelberg, 2012.

As an open resource, the **BVPh
1.0** can be free downloaded at the following hyperlinks. The higher version of the **BVPh** will be issued in future.

**Source Code: **Text form

Zip form of BVPh 1.0 (for Mathematica
5.2)

Zip form of BVPh 1.1 (for Mathematica
8.0)

Zip
form of BVPh 1.2 (for
Mathematica 8.0)

**Input Data Files of Examples:**

Chapter
8:

Example
8.3.1 Example 8.3.2 Example 8.3.3

Chapter
9:

Example
9.3.1 Example 9.3.2 Example 9.3.3 Example
9.3.4 Example 9.3.5

Chapter
10:

Exponentially
decaying solution Algebraically decaying solution

Chapter
11:

Chapter 12: