R. Hammerling, O. Koch, C. Simon, E. Weinmüller:

"Numerical solution of singular eigenvalue problems for ODEs with a focus on problems posed on semi-infinite intervals";

in: "ASC Report 08/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

This work is concerned with the computation of eigenvalues and eigenfunctions of singular

eigenvalue problems (EVPs) arising in ordinary differential equations.

Two different numerical methods to determine values for the eigenparameter such that

the boundary value problem has nontrivial solutions are considered.

The first approach incorporates a collocation method. In the course of this work the existing

code bvpsuite designed for the solution of boundary value problems was extended

by a module for the computation of eigenvalues and eigenfunctions.

The second solution approach represents a matrix method.

A code for first order problems is realized in such a way that problems of higher order

can also be solved after a transformation to the first order formulation.

Since many eigenvalue problems are of second order, for example Sturm-Liouville problems,

we also implemented a code for second order problems and present an empirical

error analysis.

For the solution of semi-infinite interval problems a transformation of the independent

variable is carried out in such a way that the boundary value problem (BVP) originally

posed on a semi-infinite interval is reduced to a singular problem posed on a finite interval.

The implementation of this transformation is also incorporated into the bvpsuite

package.

The time-independent Schrödinger equation serves as an illustrating example

http://www.asc.tuwien.ac.at/preprint/2010/asc08x2010.pdf

Created from the Publication Database of the Vienna University of Technology.