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G. Kitzhofer, O. Koch, G. Pulverer, C. Simon, E. Weinmüller:
"The new MATLAB code bvpsuite for the solution of singular implizit BVPs";
in: "ASC Report 03/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

Our aim is to provide the open domain MATLAB code bvpsuite for the efficient numerical
solution of boundary value problems (BVPs) in ordinary differential equations (ODEs). Motivated
by applications, we are especially interested in designing a code whose scope is appropriately wide,
including fully implicit problems of mixed orders, parameter dependent problems, problems with
unknown parameters, problems posed on semi-infinite intervals, eigenvalue problems (EVPs) and
differential algebraic equations (DAEs) of index 1. Our main focus is on singular BVPs in which
singularities in the differential operator arise. We first shortly recapitulate the analytical properties of
singular systems and the convergence behavior of polynomial collocation used as a basic solver in the
code for both singular and regular ODEs and DAEs. We also discuss the a posteriori error estimate
and the grid adaptation strategy implemented in our code. Finally, we describe the code structure and
present the performance of the code which has been equipped with a graphical user interface (GUI)
for an easy use.

Boundary value problems - singularity of the first kind - singularity of the second kind

http://www.asc.tuwien.ac.at/preprint/2010/asc03x2010.pdf