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Numerische Mathematik

, Volume 65, Issue 1, pp 407–421 | Cite as

Collocation methods for differential-algebraic equations of index 3

  • Laurent Jay
Article

Summary

This article give sharp convergence results for stiffly accurate collocation methods as applied to differential-algebraic equations (DAE's) of index 3 in Hessenberg form, proving partially a conjecture of Hairer, Lubich, and Roche.

Mathematics Subject Classification (1991)

65L06 

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References

  1. 1.
    Brenan, K.E., Campbell, S.L., Petzold, L.R. (1989): Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. North-Holland New YorkGoogle Scholar
  2. 2.
    Brenan, K.E., Petzold, L.R. (1989): The numerical solution of higher index differential algebraic equations by implicit Runge-Kutta methods. SIAM J. Numer. Anal.26, 976–996Google Scholar
  3. 3.
    Hairer, E., Lubich, C., Roche, M. (1989) The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods. Lect. Notes Math.1409 Google Scholar
  4. 4.
    Hairer, E., Nørsett, S.P., Wanner, G. (1987): Solving Ordinary Differential Equations I. Nonstiff Problems. Comput. Math.8 Google Scholar
  5. 5.
    Hairer, E., Wanner, G. (1991): Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Comput. Math.14 Google Scholar
  6. 6.
    Lubich, C. (1992): Imegration of stiff mechanical systems by Runge-Kutta methods Report, SAM/ETH, ZürichGoogle Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Laurent Jay
    • 1
  1. 1.Département de mathématiquesUniversité de GenèveGenève 24Switzerland

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