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G. Kitzhofer, O. Koch, E. Weinmüller:
"Pathfollowing for essentially singular boundary value problems with application to the complex Ginzburg-Landau equation";
in: "ASC Report 19/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

We discuss a pathfollowing strategy based on pseudo-arclength parametrization for
the solution of parameter-dependent boundary value problems for ordinary differential
equations. We formulate criteria which ensure the successful application of this
method for the computation of solution branches with turning points for problems
with an essential singularity. Finally, we demonstrate that a Matlab implementation
of the solution method based on an adaptive collocation scheme is well suited to solve
problems of practical relevance. As one example, we compute solution branches for
the complex Ginzburg-Landau equation which start from multi-bump solutions of
the nonlinear Schr¨odinger equation. Following the branches around turning points,
real-valued solutions of the nonlinear Schr¨odinger equation can easily be computed.

Boundary value problems for ordinary differential equations, essential

http://asc.tuwien.ac.at/preprint/2007/asc19x2007.pdf