Contractivity preserving explicit linear multistep methods (Q1105991)

We investigate contractivity properties of explicit linear multistep methods in the numerical solution of systems of ordinary differential equations. The emphasis is on the general test-equation \(d/dtU(t)=AU(t)\), where A is a square matrix of arbitrary order \(s\geq 1\). The contractivity is analysed with respect to arbitrary norms in the s-dimensional space (which are not necessarily generated by an inner product). For given order and step number we construct optimal multistep methods allowing the use of a maximal stepsize.