Paper Info
Title
Convergence of collocation schemes for boundary value problems in nonlinear index 1 DAEs with a singular point.
Abstract
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 certain class of well-posed boundary value problems in DAEs having a sufficiently smooth solution, the global error of the collocation scheme converges uniformly with the so-called stage order. Due to the singularity, superconvergence at the mesh points does not hold in general. The theoretical results are supported by numerical experiments.
Year
DOI
Venue
2013
10.1090/S0025-5718-2012-02637-8
MATHEMATICS OF COMPUTATION
Field
DocType
Volume
Singular point of a curve,Boundary value problem,Mathematical optimization,Nonlinear system,Polynomial,Mathematical analysis,Superconvergence,Singularity,Ode,Mathematics,Collocation
Journal
82
Issue
ISSN
Citations 
282
0025-5718
0
PageRank 
References 
Authors
0.34
6
4
Name
Order
Citations
PageRank
Alexander Dick100.34
Othmar Koch217428.41
Roswitha März32510.56
Ewa Weinmüller411824.75