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W. Auzinger, O. Koch, J. Petrickovic, E. Weinmüller:
"Numerical Solution of Boundary Value Problems with an Essential Singularity";
Report for ANUM Preprint No. 3/03; 2003.

Singular boundary value problems with a singularity of the first kind frequently occur in applications, e.g. when a partial differential equation PDE is reduced to an ordinary differential equation in the presence of symmetries. More difficult problems featuring a singularity of the second kind (essential singularity) arise, for instance, when a boundary value ODE is transformed from an infinite interval to a finite one. They are also very common in quantum physics, mechanics, investigations of ferromagnetic systems (e.g. Ginzburg-Landau equations) etc.
In this work we present a study of certain numerical techniques - which are well known to perform efficiently and accurately in the case of a singularity of the first kind - applied to problems with an essential singularity. In particular, collocation methods are considered together with a posteriori error estimates intended to provide the basis for a grid selection strategy.

http://www.math.tuwien.ac.at/~winfried/papers/anumpp0303.pdf