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Contractivity-preserving implicit linear multistep methods


Author: H. W. J. Lenferink
Journal: Math. Comp. 56 (1991), 177-199
MSC: Primary 65L06; Secondary 65L20
DOI: https://doi.org/10.1090/S0025-5718-1991-1052098-0
MathSciNet review: 1052098
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Abstract: We investigate contractivity properties of implicit linear multistep methods in the numerical solution of ordinary differential equations. The emphasis is on nonlinear and linear systems $ \frac{d}{{dt}}U(t) = f(t,U(t))$, where f satisfies a so-called circle condition in an arbitrary norm. The results for the two types of systems turn out to be closely related. We construct optimal multistep methods of given order and stepnumber, which allow the use of a maximal stepsize.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1991-1052098-0
Article copyright: © Copyright 1991 American Mathematical Society

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