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R. Hammerling, O. Koch, C. Simon, E. Weinmüller:
"Numerical treatment of singular ODE EVPs using bvpsuite";
in: "ASC Report 16/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

We put forward a new method for the solution of eigenvalue problems for (systems of) ordinary differential
equations, where our main focus is on eigenvalue problems for singular Schrödinger equations arising, for example, in
electronic structure computations. Here, the generation of the starting values for the computation of eigenvalues of higher
index is a critical issue. Our approach comprises two stages: First we generate rough approximations by a matrix method.
These approximations are used as starting values for an adaptive collocation method which yields approximations of high
accuracy together with a reliable error estimate. We successfully apply our method to the solution of the coupled ODE Stark
problem for the hydrogen atom.

electronic structure computation - polynomial collocation - fullpotential core solver - singular eigenvalue problems

http://www.asc.tuwien.ac.at/preprint/2010/asc16x2010.pdf