Hanke, Michael ;Izquierdo Macana, Ebroul; März, Roswitha
On asymptotics in case of linear index-2 differential-algebraic equations
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods

34D20 Lyapunov stability

Abstract: Asymptotic properties of solutions of general linear differential-algebraic equations (DAE's) 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 DAE's are given. The behaviour of BDF, IRK, and PIRK 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.
Keywords: differential-algebraic equation, stability, asymptotic properties, Runge-Kutta method, backward differentiation formulas