Numerically well formulated index-1 DAEs

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

65L80 Methods for differential-algebraic equations

34A09 Implicit equations, differential-algebraic equations

Abstract
For index-1 DAEs with properly stated leading term, we characterize dissipative and contractive flows and study how the qualitative properties of the DAE solutions are reflected by numerical approximations. The best situation occurs when the discretization and the decoupling procedure commute. It turns out out that this is the case if the relevant part of the inherent regular ODE has a constant state space. Different kinds of reformulations are studied to obtain numerically well formulated systems. Those reformulations might be expensive, hence, in order to avoid them, criteria ensuring the given DAE to be numerically equivalent to a numerically well formulated representation are proved.

Keywords: differential algebraic equations, numerical integration methods, global stability