BIT Numerical Mathematics

, Volume 15, Issue 4, pp 358–361

A stability property of implicit Runge-Kutta methods

  • J. C. Butcher


A class of implicit Runge-Kutta methods is shown to possess a stability property which is a natural extension of the notion ofA-stability for non-linear systems.


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    G. Dahlquist,Error Analysis for a Class of Methods for Stiff Non-linear Initial Value Problems, to be published in the Proceedings of the Conference on Numerical Analysis, Dundee, 1975.Google Scholar
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    J. C. Butcher,Implicit Runge-Kutta Processes, Math. Comp. 18 (1964), 50–64.Google Scholar
  3. 3.
    B. L. Ehle,On Padé Approximation to the Exponential Function and A-stable Methods for the Numerical Solution of Initial Value Problems Research Report CSRR 2010, Dept. AACS, University of Waterloo.Google Scholar
  4. 4.
    F. H. Chipman,A-stable Runge-Kutta Processes, BIT 11 (1971), 384–388.Google Scholar

Copyright information

© BIT Foundations 1975

Authors and Affiliations

  • J. C. Butcher
    • 1
  1. 1.Department of MathematicsUniversity of AucklandAucklandNew Zealand

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