Stability preserving integration of index-1 DAEs. (Q1874215)

The paper is concerned with differential-algebraic equations (DAEs) of index 1 and their numerical integration. The main topic is the investigation of conditions under which certain qualitative properties of the DAE, in particular contractivity or dissipativity, are properly reflected by their numerical approximations without stepsize restriction, when numerical schemes with suitable stability properties are used. For this purpose, the DAE is required to have a ``properly stated leading term'' and to be ``numerically qualified''. But also for not numerically qualified DAE's, equivalent reformulations can help to obtain the desired properties, as is illustrated in several examples.