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A. Dick, O. Koch, R. März, E. Weinmüller:
"Convergence of collocation schemes for nonlinear index 1 DAEs with a singular point";
in: "ASC Report 13/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

We analyze 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 well-posed boundary value problem in DAEs having a sufficiently
smooth solution, the global error of the collocation scheme converges with the so-called stage order. Due
to the singularity, superconvergence does not hold in general. The theoretical results are supported by
numerical experiments.

http://www.asc.tuwien.ac.at/preprint/2010/asc13x2010.pdf