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W. Auzinger, O. Koch, E. Weinmüller:
"Numerical solution of singular boundary value problems in ordinary differential equations";
Talk: Österreichisch-Mongolischer Mathematikertag, TU Wien (invited); 2007-10-01 - 2007-10-02.

We consider analytical properties and the numerical treatment of boundary value problems in ordinary differential equations with a time singularity. First, well-posedness and smoothness of the solution is discussed for the analytical problem. Subsequently, we describe the numerical treatment by collocation methods. After giving a convergence result, we introduce and analyze a new estimate for the global discretization error based on the defect correction principle. These components are the basis of successful software for singular boundary value problems developed by our group. This additionally features adaptive mesh selection by equidistribution of the global error and can also be successfully applied to solve differential algebraic equations, implicit problems, and problems with known or unknown parameters. The success of our solution approach is illustrated by virtue of examples including the computation of self-similar blow-up solutions of nonlinear PDEs and the density profile equation in hydrodynamics.

Singular boundary value problems, analysis, numerical methods

http://dx.doi.org/10.1016/j.cam.2004.10.013

Project Head Ewa Weinmüller:
Programm zur Lösung singulärer Randwert/