Remodeling of Dynamical Systems to Benefit Numerical Simulations

Differential-algebraic equations (DAEs) are essential tools in the modeling of dynamical processes. For instance, the dynamical behavior of mechanical systems, electrical circuits and many other are often described by DAEs, in particular, of quasi-linear structure. In this article we consider dynamical systems modeled with quasi-linear DAEs of higher index, with respect to their remodeling in view of an efficient and robust numerical simulation. We will present an iterative procedure which provides a general tool for the remodeling of dynamical systems, i.e., a regularization of quasi-linear DAEs of an arbitrary index. This procedure regularizes a quasi-linear DAE by an iterative lowering of the index while maintaining all constraints, in particular, the hidden constraints. The procedure ends with the projected-strangeness-free form of the quasi-linear DAE which can be used as basis for numerical simulations or further numerical investigations of the dynamical system.Furthermore, the basic idea to simulate such remodeled systems in an efficient and robust way will be discussed and illustrated by an example using the software package GEOMS.