Inmaculada Higueras,
Roswitha März,
Caren Tischendorf
Preprint series:
Institut für Mathematik, HumboldtUniversität zu Berlin (ISSN 08630976),
MSC 2000
 65L80 Methods for differentialalgebraic equations

34A09 Implicit equations, differentialalgebraic equations
Abstract
For index1 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