Regularization of nonlinear DAEs based on Algebraic Analysis

Abstract

Differential-algebraic equations (DAEs) arise naturally in many technical and industrial applications. In particular, in automatic modeling using coupling of modularized subcomponents, the coupling of subcomponents is usually described by algebraic constraints which lead to DAEs as model equations. The direct numerical integration of DAEs in general is not feasible due to so-called hidden constraints which are contained in the DAE. The occurrence of hidden constraints leads to difficulties in the numerical integration as instabilities or order reduction can occur. Therefore, it is necessary to regularize or remodel the model equations before a robust numerical integration is possible. We review a remodeling or regularization techniques for general nonlinear DAEs based on an algebraic analysis that has been developed in Kunkel and Mehrmann (2001). This technique can be used to improve the model equations for the numerical treatment.