Linear constant coefficient DAEs

Abstract

This chapter represents an introduction into the projector based framework by means of well-understood constant coefficient DAEs. In particular, we demonstrate that all components of the Kronecker structure of a regular matrix pencil can be described by so-called admissible matrix sequences and their associated projectors. We provide a complete decoupling of the DAE into its slow and fast subsystems by this technique. Thereby we do not transform the DAE itself, instead we express all system coefficients and characteristics in terms of the matrix sequence which is directly computed from the original matrix pencil. The spectral projector of the matrix pencil, for instance, results as a product of completely decoupling projectors.