Recently Ch. Lubich proved convergence results for Runge-Kutta methods applied to stii mechanical systems. The present paper discusses the new ideas necessary to extend these results to general linear methods, in particular BDF and multistep Runge-Kutta methods. Stii mechanical systems arise in the modelling of mechanical systems containing strong springs and (or) elastic joints. A typical exam...

The subject matter of this paper is the recovery of invariants and conservation laws of ordinary diierential systems by numerical methods. We prove that the most likely candidates for this task, Runge{Kutta schemes, fail to stay on manifolds deened by r-tensors with r 3. As an alternative, we suggest diieomorphically mapping complicated man-ifolds to simpler ones. This procedure allows for reco...

This paper is concerned with time-stepping numerical methods for computing stii semi-discrete systems of ordinary diierential equations for transient hyper-sonic ows with thermo-chemical nonequilibrium. The stiiness of the equations is mainly caused by the vis-cous ux terms across the boundary layers and by the source terms modeling nite-rate thermo-chemical processes. Implicit methods are need...