Inmaculada Higueras, Roswitha März, Caren Tischendorf
Preprint series: Institut für Mathematik, Humboldt-Universität
zu Berlin (ISSN 0863-0976), 01-10
MSC 2000
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65L80 Methods for differential-algebraic equations
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65L06 Multistep, Runge-Kutta and extrapolation methods
Abstract
For
linear index-2 DAEs with properly stated leading term we characterize contractive
and dissipative flows. We study under which conditions the qualitative
properties of the DAE solutions are reflected by the numerical approximations.
This is the case if the discretisation and the decoupling processes commute.
Commutativity is achieved if two subspaces associated with the index-2
DAE are constant; in this case we say that the index-2 DAE is numerically
well formulated. If both subspaces are time dependent, the problem should
be reformulated; in order to avoid numerically equivalent reformulations,
a criterion is given. If only one of these subspaces is constant, the problem
is in some sense close to a numerically well formulated one and thus depending
on the problem context, no reformulations are needed. Contractive and dissipative
flows induced by the DAE are characterized and results on qualitative properties
of the numerical solution are given.
Keywords:differential
algebraic equations, DAE, numerical integration methods,global stability,
BDF, Runge-Kutta