Differential-Algebraic Equations: A Projector Based Analysis

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.

New comprehensive analysis of general nonlinear DAEs First book describing the projector approach for nonlinear, higher-index DAEs Rigorous description, multitude of examples highlighting analytical and numerical challenges in this field Suitable for students, researchers and users from different application fields (e.g. circuit and electromagnetic simulation, mechanical engineering, system biology) Includes supplementary material: sn.pub/extras

Autorentext

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

Inhalt
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.