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 orders≧1. 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.
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This research has been supported by the Netherlands organisation for scientific research (NWO)
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Lenferink, H.W.J. Contractivity preserving explicit linear multistep methods. Numer. Math. 55, 213–223 (1989). https://doi.org/10.1007/BF01406515
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DOI: https://doi.org/10.1007/BF01406515