O. Koch, R. März, D. Praetorius, E. Weinmüller:
"Collocation Methods for Index 1 DAEs with a Singularity of the First Kind";
Math. Comp., 79 (2010), S. 281 - 304.

Kurzfassung englisch:
We study the convergence behavior of collocation schemes applied to
approximate solutions of BVPs in linear index 1 DAEs which exhibit a
critical point at the left boundary. Such a critical point of the DAE
causes a singularity within the inherent ODE system. We focus our
attention on the case when the inherent ODE system is singular with a
singularity of the first kind, apply polynomial collocation to the
original DAE system and consider different choices of the collocation
points such as equidistant, Gaussian or Radau points. We show that
for a well-posed boundary value problem for DAEs having a
sufficiently smooth solution, the global error of the collocation
scheme converges with the order $O(h^s)$, where $s$ is the number of
collocation points. Superconvergence cannot be expected in general
due to the singularity, not even for the differential components of
the solution. The theoretical results are illustrated by numerical

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