Session on DAEs and their Applications

摘要

After more than 30 years of investigations and the pioneering work of Bill Gear and Linda R. Petzold, the field of Differential-Algebraic Equations (DAEs) is still an exciting research area. The aim of this session is to bring together top-notch scientists with interests in the mathematical theories, numerical methods, and applications of DAEs. The term algebraic in the terminology of DAEs may be misleading to the novice. What is generally meant by DAEs are constrained systems of differential equations or differential equations on manifolds. Mathematically simply speaking, DAEs are systems which can be expressed in the form R(t,y,dy/dt)=0. Many problems from science and engineering can be more easily formulated as DAEs than as Ordinary Differential Equations (ODEs) dy/dt=f(t,y). Existence and uniqueness of solutions to DAEs cannot be as easily expressed as for ODEs. There are basically two classes of DAEs: DAEs with specific structures such as those arising in mechanics and circuit simulation, and DAEs where no or very little structure is a priori specified. Research in DAEs has gone in these two directions from both mathematical and numerical points of view. Although the theory of DAEs is quite important for the theory of stiff ODEs, there is a well-known saying that DAEs are not ODEs. One can emphasize this point by claiming that good methods for DAEs are not necssarily related to good methods for stiff ODEs. On the special occasion of Ernst Hairer' 60th birthday we would like to recognize his many brilliant contributions to the theory of DAEs and their dissemination through his superb books.