BIT Numerical Mathematics

, Volume 27, Issue 4, pp 510–533 | Cite as

The equivalence of algebraic stability andAN-stability

  • J. C. Butcher
Part II Numerical Mathematics


It is shown that, under certain restrictions,AN-stability is equivalent to algebraic stability for general linear methods. The restrictions have the purpose of excluding from consideration methods which can be replaced by simpler methods in various specific ways andAN-stability is to be interpreted in the strong sense. This result generalizes known results for Runge-Kutta and for one-leg methods.

CR classification


AMS classification



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Copyright information

© BIT Foundations 1987

Authors and Affiliations

  • J. C. Butcher
    • 1
  1. 1.Department of Computer ScienceUniversity of AucklandAucklandNew Zealand

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