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.

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

experiments.

http://dx.doi.org/10.1090/S0025-5718-09-02267-4

Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.