On Asymptotics in Case of Linear Index-2 Differential-Algebraic Equations

Asymptotic properties of solutions of general linear differential-algebraic equations (DAEs) and those of their numerical counterparts are discussed. New results on the asymptotic stability in the sense of Lyapunov as well as on contractive index-2 DAEs are given. The behavior of the backward differentiation formula (BDF), implicit Runge--Kutta (IRK), and projected implicit Runge--Kutta (PIRK) methods applied to such systems is investigated. In particular, we clarify the significance of certain subspaces closely related to the geometry of the DAE. Asymptotic properties like A-stability and L-stability are shown to be preserved if these subspaces are constant. Moreover, algebraically stable IRK(DAE) are B-stable under this condition. The general results are specialized to the case of index-2 Hessenberg systems.