BIT Numerical Mathematics

, Volume 25, Issue 1, pp 285–288 | Cite as

A necessary condition forBSI-stability

  • Kees Dekker
  • Ernst Hairer
Scientific Notes


This paper gives a negative result onBSI-stability for the Lobatto IIIC-methods with more than two stages. We also give a necessary condition forBSI-stability.


Computational Mathematic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. H. Chipman,A-stable Runge-Kutta processes, BIT 11 (1971), 384–388.Google Scholar
  2. 2.
    M. Crouzeix, W. H. Hundsdorfer and M. N. Spijker,On the existence of solutions to the algebraic equations in Runge-Kutta methods, BIT 23 (1983), 84–91.Google Scholar
  3. 3.
    K. Dekker,Error bounds for the solution to the algebraic equations in Runge-Kutta methods, BIT 24 (1984), 347–356.Google Scholar
  4. 4.
    K. Dekker and J. G. Verwer,Stability of Runge-Kutta methods for stiff nonlinear differential equations. North-Holland Publ. Co, Amsterdam (1984).Google Scholar
  5. 5.
    R. Frank, J. Schneid and C. W. Ueberhuber,Stability properties of implicit Runge-Kutta methods (to appear in SIAM J. Numer. Anal.).Google Scholar
  6. 6.
    E. Hairer and G. Wanner,Algebraically stable and implementable Runge-Kutta methods of high order, SIAM J. Numer. Anal. 18 (1981), 1098–1108.CrossRefGoogle Scholar
  7. 7.
    W. H. Hundsdorfer and M. N. Spijker,On the algebraic equations in implicit Runge-Kutta methods, Report NM-R8413, Centre for Math. and Computer Science, Amsterdam (1984).Google Scholar
  8. 8.
    J. I. Montijano,Estudio de los metodos SIRK para la resolucion numérica de ecuaciones differenciales de tipo stiff, Thesis, University of Zaragoza (1983).Google Scholar

Copyright information

© BIT Foundations 1985

Authors and Affiliations

  • Kees Dekker
    • 1
    • 2
  • Ernst Hairer
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of LeidenLeidenThe Netherlands
  2. 2.Institut für Angewandte MathematikUniversität HeidelbergHeidelbergBRD

Personalised recommendations