Contributions to Books:

O. Koch, R. März, D. Praetorius, E. Weinmüller:
"Collocation methods for index 1 DAEs with a singularity of the first kind";
in: "ASC Report 10/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8.

English abstract:
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
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 so-called stage order, or equivalently, it is O(h^m), where
m 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 experiments.

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.