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Symmetric collocation for unstructured nonlinear differential-algebraic equations of arbitrary index

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Summary.

We examine a class of symmetric collocation schemes for the solution of nonlinear boundary value problems for unstructured nonlinear systems of differential-algebraic equations with arbitrary index. We show that these schemes converge with the same orders as one would expect for ordinary differential equations. In particular, we show superconvergence for a special choice of the collocation points. We demonstrate the efficiency of the new approach with some numerical examples.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Leipzig, Augustusplatz 10-11, 04109, Leipzig, Germany

    Peter Kunkel

  2. Institut für Mathematik, MA 4-5, TU Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Volker Mehrmann

  3. Zentrum für Technomathematik, Fachbereich 3, Universität Bremen, Postfach 330 440, 28334, Bremen, Germany

    Ronald Stöver

Authors
  1. Peter Kunkel
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  2. Volker Mehrmann
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  3. Ronald Stöver
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Correspondence to Peter Kunkel.

Additional information

Mathematics Subject Classification (2000): 65L10

Revised version received November 21, 2003

Supported by DFG research grant Ku964/4.

Supported by DFG research grant Me790/11.

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Kunkel, P., Mehrmann, V. & Stöver, R. Symmetric collocation for unstructured nonlinear differential-algebraic equations of arbitrary index. Numer. Math. 98, 277–304 (2004). https://doi.org/10.1007/s00211-004-0534-9

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  • DOI: https://doi.org/10.1007/s00211-004-0534-9

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