Preprint 11-2006

Analysis of Quasi-Linear Differential-Algebraic Equations

Author(s) : Andreas Steinbrecher

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 11-2006

MSC 2000

65L80 Methods for differential-algebraic equations

65L05 Initial value problems

Abstract :
In this report we will discuss in detail quasi-linear DAEs with respect to their analytical properties. As first instance, we will review fundamental basics, in particular, we review the differential index, the strangeness index, and some important properties of strangeness-free quasi-linear DAEs. Furthermore, we will present a procedure which provides a general tool for the investigation of general quasi-linear DAEs of an arbitrary index. This procedure offers the possibility for the determination of the differentiation index, the determination of a lower bound of the strangeness index as well as the definition of the hidden constraints, the maximal constraint level, and the solution manifold.

Keywords : hidden constraints, maximal constraint level, quasi-linear differential-algebraic equations, strangeness index