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Numerische Mathematik

, Volume 88, Issue 4, pp 771–795 | Cite as

Collocation methods for solving linear differential-algebraic boundary value problems

  • Ronald Stöver
Original article

Summary.

We consider boundary value problems for linear differential-algebraic equations with variable coefficients with no restriction on the index. A well-known regularisation procedure yields an equivalent index one problem with d differential and a=n-d algebraic equations. Collocation methods based on the regularised BVP approximate the solution x by a continuous piecewise polynomial of degree k and deliver, in particular, consistent approximations at mesh points by using the Radau schemes. Under weak assumptions, the collocation problems are uniquely and stably solvable and, if the unique solution x is sufficiently smooth, convergence of order min {k+1,2k-1} and superconvergence at mesh points of order 2k-1 is shown. Finally, some numerical experiments illustrating these results are presented.

Mathematics Subject Classification (1991): 65L10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Ronald Stöver
    • 1
  1. 1.Universität Bremen, Fachbereich 3 – Mathematik und Informatik, Postfach 330 440, 28334 Bremen, Germany; e-mail: stoever@math.uni-bremen.de DE

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