Regularization of Quasi-Linear Differential-Algebraic Equations

Abstract

The complete virtual design of dynamical systems, e.g., mechanical systems, electrical circuits, flow problems, or whole production processes, plays a key role in our technological progress. In this context differential-algebraic equations (DAEs) are a very important tool for the analysis and simulation of such dynamical processes. It is well known that the numerical treatment of DAEs is nontrivial in general. The occurrence of hidden constraints (contained in the DAE but only obtainable by differentiating of (parts of) the DAE) impose additional consistency conditions on the initial values and provoke severe difficulties in the direct numerical integration of DAEs as for example drift, instabilities, or convergence problems. Therefore, it is necessary to regularize or remodel the model equations before a robust numerical integration is possible.In this article we present regularization methods for quasi-linear DAEs. In particular, we discuss the projected strangeness-free formulation, the minimally extended formulation, and the overdetermined formulation as regularizations. At the end we give some remarks on the numerical treatment of the presented regularizations.