Synopses & Reviews
Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980's, no more than about three decades ago. In this relatively short time, DAEs have become a widely acknowledged tool to model processes subjected to constraints, in order to
Synopsis
This book analyzes the impressive complexity of Differential algebraic equations (DAEs), to describe the state of the art and to examine open problems, thus to motivate further research on this versatile topic from a broader mathematical perspective.
About the Author
Dr. René Lamour, Humbold University of Berlin, Department of Mathematics, Germany Prof. Dr. Roswitha März, Humbold University of Berlin, Department of Mathematics, Germany Prof. Dr. Caren Tischendorf, University of Cologne, Mathematical Institute, Germany
Table of Contents
Notations.- Introduction.- Part I. Projector based approach.- 1 Linear constant coefficient DAEs.-.2 Linear DAEs with variable coefficients.- 3 Nonlinear DAEs.- Part II. Index-1 DAEs: Analysis and numerical treatment.- 4 Analysis.- 5 Numerical integration.- 6 Stability issues.- Part III. Computational aspects.- 7 Computational linear algebra aspects.- 8 Aspects of the numerical treatment of higher index DAEs.- Part IV. Advanced topics.- 9 Quasi-regular DAEs.- 10 Nonregular DAEs.- 11 Minimization with constraints described by DAEs.- 12 Abstract differential algebraic equations.- A. Linear Algebra - Basics.-.B. Technical Computations.- C Analysis.- References.- Index.