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Contractivity preserving explicit linear multistep methods
Authors:H W J Lenferink
Institution:(1) Department of Mathematics and Computer Science, University of Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
Abstract:Summary We investigate contractivity properties of explicit linear multistep methods in the numerical solution of ordinary differential equations. The emphasis is on the general test-equation 
$$\frac{d}{{dt}}U(t) = AU(t)$$
, whereA is a square matrix of arbitrary ordersgE1. The contractivity is analysed with respect to arbitrary norms in thes-dimensional space (which are not necessarily generated by an inner product). For given order and stepnumber we construct optimal multistep methods allowing the use of a maximal stepsize.This research has been supported by the Netherlands organisation for scientific research (NWO)
Keywords:AMS(MOS): 65L05  65L20  65M10  CR: G  1  7  G  1  8
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