A special stability problem for linear multistep methods
- Germund G. Dahlquist
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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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- A special stability problem for linear multistep methods
BIT Numerical Mathematics
Volume 3, Issue 1 , pp 27-43
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- Kluwer Academic Publishers
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- 1. Royal Institute of Technology, Stockholm, Sweden