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BIT Numerical Mathematics

, Volume 15, Issue 4, pp 358–361 | Cite as

A stability property of implicit Runge-Kutta methods

  • J. C. Butcher
Article

Abstract

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.

Keywords

Computational Mathematic Stability Property Natural Extension 
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.

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References

  1. 1.
    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
  2. 2.
    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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