Analyzing the stability behaviour of DAE solutions and their approximations

Abstract

New stability results are proved for linear index-2 differential algebraic equations (DAE). They are obtained by means of an improved projector decoupling. On the background of logarithmic norms related to invariant subspaces, contractivity is considered. The asymptotical behaviour of approximations generated by the BDF as well as by IRK and PIRK methods is analyzed in some detail. In particular, under weaker invariance conditions than used by Hanke, Macana and Maerz (1998), it is shown that standard properties known from the case of regular ODEs like A-stability, B-stability etc. apply also to index-2 DAEs. Moreover, the same invariance condition permits index reduction by differentiating constraints and discretization to commute.