Contractivity preserving explicit linear multistep methods

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 , whereA is a square matrix of arbitrary orders1. 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)