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BIT Numerical Mathematics

, Volume 13, Issue 2, pp 153–159 | Cite as

A new class of highly-stable methods:A0-stable methods

  • Colin W. Cryer
Article

Abstract

A linear multistep method (ζ,σ) is defined to beA0-stable if when it is applied to the equation\(\dot x(t) = - \lambda x(t)\) the approximate solutionx h (t n ) tends to zero ast n → ∞ for all values of the stepsizeh and allλ∈(0, ∞).

Various properties ofA0-stable methods are derived. It is shown that most of the properties ofA(α)-stable methods are shared byA0-stable methods. It is proved that there existA0-stable methods of arbitrarily high order.

Keywords

Computational Mathematic Stable Method Multistep Method Linear Multistep Method 
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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Copyright information

© BIT Foundations 1973

Authors and Affiliations

  • Colin W. Cryer
    • 1
  1. 1.Computing LaboratoryOxford UniversityOxfordEngland

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