Roswitha März
Preprint series: Institut für Mathematik, Humboldt-Universität
zu Berlin (ISSN 0863-0976), 29
MSC 2000
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65L80 Methods for differential-algebraic equations
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65L06 Multistep, Runge-Kutta and extrapolation methods
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34A09 Implicit equations, differential-algebraic equations
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49J27 Problems in abstract spaces
Abstract
Linear
differential algebraic equations with properly stated leading term are
considered via a decoupling into their essential parts. It is shown why
for so-called numerically well formulated equations the decoupling and
discretizations commute in some sense. In general one can not expect this
commutativity so that additional difficulties like strong stepsize restrictions
may arise. Moreover, abstract differential algebraic equations in infinite
dimensional Hilbert spaces are discussed. In particular, a linear-quadratic
control problem for those equations is proved to be solvable.
Keywords:Differential
algebraic equations, numerical integration methods, linear-quadratic control,
abstract differential algebraic