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G. Kitzhofer, O. Koch, G. Pulverer, C. Simon, E. Weinmüller:
"BVPSUITE: a new MATLAB solver for singular implicit boundary value problems";
in: "ASC Report 35/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5, 411 - 424.

Our aim is to provide an open domain Matlab code bvpsuite for the efficient numerical solution of
boundary value problems (BVPs) in ordinary differential equations (ODEs). Motivated by applica-
tions, 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 parame-
ters, 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 dif-
ferential 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 posteriori error estimate and the grid adaptation
strategy implemented in our code. Finally, we describe the code structure, input/output parameters,
and present the performance of the code. We provide numerical examples to help using our software
package, especially the graphical user interface (GUI).

http://dx.doi.org/10.1007/s10915-005-9020-5

http://www.asc.tuwien.ac.at/preprint/2009/asc35x2009.pdf