J. Cash, G. Kitzhofer, O. Koch, G. Moore, E. Weinmüller:

"Numerical Solution of singular two point BVPs";

in: "ASC Report 22/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8.

An algorithm is described for the efficient numerical solution of singular two-point boundary value problems.

The algorithm is based on collocation at Gauss points, is applied directly to second order equations

and uses a transformation of the independent variable to obtain extra smoothness if needed. Numerical

comparisons between a code based on this approach and codes based on other options which have previously

been thought of as possible alternatives such as collocation at Lobatto points or reduction to a

first order system, are made and the efficiency of the new approach is clearly demonstrated by numerical

results.

http://www.asc.tuwien.ac.at/preprint/2008/asc22x2008.pdf

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