Stability questions for differential-algebraic equations

C. Tischendorf, University of Köln, Germany

Wednesday, April 8
at 16.15, HG E 1.2

The numerical integration of differential-algebraic equations (DAEs) is sometimes accompanied by effects that we do not expect concerning the knowledge from the integration of ordinary differential equations. One of such effects is the observation that implicit methods behave like explicit ones. In certain cases we need very small stepsizes in order to get an asymptotically correct solution even if we apply A-stable methods. Such an effect has been reported already by U. Ascher and L. Petzold in 1993, however without finding the reason for it.

Here we present an explanation for this behavior. We show that the formulation of differential-algebraic equations may have a strong influence onto the asymptotical behavior of numerical solutions. Furthermore, we discuss the question of A-stability for DAEs. Finally, we explain how circuit simulation systems can be formulated such that one avoids numerical instabilities.