Differential algebraic systems anew

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.