A special stability problem for linear multistep methods

@article{Dahlquist1963ASS,
  title={A special stability problem for linear multistep methods},
  author={Germund Dahlquist},
  journal={BIT Numerical Mathematics},
  year={1963},
  volume={3},
  pages={27-43}
}
  • G. Dahlquist
  • Published 1 March 1963
  • Mathematics
  • BIT Numerical Mathematics
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. 
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From the Publisher: For this inexpensive paperback edition of a groundbreaking classic, the author has extensively rearranged, rewritten and enlarged the material. Book is unique in its emphasis on
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  • 1962
Stability questions for some numerical methods for ordinary differential equations
  • To appear in Proc. Symposia on Applied Mathematics,
  • 1962