DAEs in applications

Abstract

Differential-algebraic equations (DAEs) arise naturally in many technical and industrial applications. By incorporating the special structure of the DAE systems arising in certain physical domains, the general approach for the regularization of DAEs can be efficiently adapted to the system structure. We will present the analysis and regularization approaches for DAEs arising in mechanical multibody systems, electrical circuit equations, and flow problems. In each of these cases the DAEs exhibit a certain structure that can be used for an efficient analysis and regularization. Moreover, we discuss the numerical treatment of hybrid DAE systems, that also occur frequently in industrial applications. For such systems, the framework of DAEs provides essential information for a robust numerical treatment.