Differential algebraic systems anew

Roswitha März

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 29

MSC 2000

65L80 Methods for differential-algebraic equations
65L06 Multistep, Runge-Kutta and extrapolation methods
34A09 Implicit equations, differential-algebraic equations
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