1D Boundary Value Problem solver for Octave and MATLAB
bvp1d solves systems of boundary value differential equations in a single spatial variable. It is mostly compatible with the MATLAB function bvp4c, one of the main differences being that it currently does not include the extra convenience functions like bvpinit. It also does not support multipoint boundary value problems or equations with complex numbers. Nevertheless, many bvp4c examples will work with bvp1d with only small changes.
The theory for bvp4c (and bvp1d) is presented in the paper by Kierzenka and Shampine.
The easiest way to get started with bvp1d and Octave is to download one of the pre-built versions from the Releases area. The bvp1d function is packaged as a single mex file for Windows, Macintosh, and Linux platforms. Several examples and basic documentation are included.
The page bvp4c by John Burkhard has several examples and links to other resources for bvp4c.
bvp1d relies on the KINSOL library from [Sundials] (http://computation.llnl.gov/projects/sundials) for solution of the nonlinear algebraic equations. In turn, KINSOL relies on the KLU sparse solver from SuiteSparse for solving sparse, linear equations. The Eigen C++ matrix class library, is used throughout the code. There is also a small dependency on the Boost C++ string package. So all of these libraries are required to build the software from scratch. The file, Makefile_octave, was used to build the versions for the three platforms in the Releases area.