Convergence of collocation schemes for boundary value problems in nonlinear index 1 DAEs with a singular point

singularity of the first kind and apply polynomial collocation to the . 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 sing...

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Bibliographic Details
Published in:Mathematics of computation 2013-04, Vol.82 (282), p.893-918
Main Authors: Alexander Dick, Othmar Koch, Roswitha März, Ewa Weinmüller
Format: Article
Language:English
Subjects:
Algebra
Boundary conditions
Boundary value problems
Eigenvalues
Mathematical problems
Odes
Ordinary differential equations
Polynomials
Textual collocation
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Summary:singularity of the first kind and apply polynomial collocation to the . 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.]]>
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-2012-02637-8