Stability preserving integration of index-1 DAEs

Authors:
I. Higueras;R. März;C. Tischendorf
Affiliations:
Universidad Pública de Navarra, Departamento de Matemática e Informática, 31006 Pamplona, Spain;Humboldt-University of Berlin, Institute of Mathematics, 10099 Berlin, Germany;Humboldt-University of Berlin, Institute of Mathematics, 10099 Berlin, Germany
Venue:
Applied Numerical Mathematics
Year:
2003

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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 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 this property. Those reformulations might be expensive, hence, in order to avoid them, criteria ensuring the given DAE to be numerically equivalent to a numerically qualified representation are proved.