Contractivity-preserving implicit linear multistep methods

Lenferink, H. W. J.

doi:10.1090/S0025-5718-1991-1052098-0

Contractivity-preserving implicit linear multistep methods
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by H. W. J. Lenferink PDF

Math. Comp. 56 (1991), 177-199 Request permission

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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