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A special stability problem for linear multistep methods

1963; Springer Science+Business Media; Volume: 3; Issue: 1 Linguagem: Inglês

10.1007/bf01963532

1572-9125

Germund Dahlquist,

Matrix Theory and Algorithms

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.