BIT Numerical Mathematics

, Volume 3, Issue 1, pp 27–43 | Cite as

A special stability problem for linear multistep methods

  • Germund G. Dahlquist


The trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. For this method error bounds are derived which are valid under rather general conditions. In order to make sure that the error remains bounded ast → ∞, even though the product of the Lipschitz constant and the step-size is quite large, one needs not to assume much more than that the integral curve is uniformly asymptotically stable in the sense of Liapunov.


General Condition Computational Mathematic Stability Problem Stability Property Error Bound 
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Copyright information

© BIT Foundations 1963

Authors and Affiliations

  • Germund G. Dahlquist
    • 1
  1. 1.Royal Institute of TechnologyStockholmSweden

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