BIT Numerical Mathematics

, Volume 3, Issue 1, pp 27–43

A special stability problem for linear multistep methods

  • Germund G. Dahlquist

DOI: 10.1007/BF01963532

Cite this article as:
Dahlquist, G.G. BIT (1963) 3: 27. doi:10.1007/BF01963532


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.

Copyright information

© BIT Foundations 1963

Authors and Affiliations

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

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