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A. Dick, O. Koch, R. März, E. Weinmüller:
"Collocation Schemes for Nonlinear Index 1 DAEs with a Singular Point";
in: "ASC Report 37/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

We discuss the convergence behavior of collocation schemes applied to approximate solutions of BVPs in nonlinear
index 1 DAEs, which exhibit a critical point at the left boundary. Such a critical point of the DAE causes a singularity in
the inherent nonlinear ODE system. In particular, we focus on the case when the inherent ODE system is singular with a
singularity of the first kind and apply polynomial collocation to the original DAE system. We show that for a certain class
of well-posed boundary value problems in DAEs having a sufficiently smooth solution, the global error of the collocation
scheme converges in the collocation points with the so-called stage order. The theoretical results are supported by numerical
experiments.

Nonlinear differential-algebraic equations; Index 1; 0-critical points; Collocation methods; Convergence

http://asc.tuwien.ac.at/preprint/2011/asc37x2011.pdf