Abstract
In 1975 the author showed that a norm (Liapunov function) can be constructed for the stability and error analysis of a linear multistep method (and the related one-leg method) for the solution of stiff non-linear systems, provided that the system satisfies a monotonicity condition and the method possesses a property calledG-stability.
In this paper it is shown thatG-stability is equivalent toA-stability. More generally, a Liapunov function exists if the stability region of the method contains a circle (half-plane), provided that the system satisfies a monotonicity condition related to this circle (half-plane). In the general case this condition depends on the stepsize.
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Dahlquist, G. G-stability is equivalent toA-stability. BIT 18, 384–401 (1978). https://doi.org/10.1007/BF01932018
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DOI: https://doi.org/10.1007/BF01932018