Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations

Preface to the Classics Edition Preface Chapter 1: Introduction. Why DAE's? Basic Types of DAE's Applications Overview Chapter 2: Theory of DAE's. Introduction Solvability and the Index Linear Constant Coefficient DAE's Linear Time Varying DAE's Nonlinear Systems Chapter 3: Multistep Methods. Introduction BDF Convergence BDF Methods, DAE's, and Stiff Problems General Linear Multistep Methods Chapter 4: One-Step Methods. Introduction Linear Constant Coefficient Systems Nonlinear Index One Systems Semi-Explicit Nonlinear Index Two Systems Order Reduction and Stiffness Extrapolation Methods Chapter 5: Software and DAE's. Introduction Algorithms and Strategies in DASSL Obtaining Numerical Solutions Solving Higher Index Systems Chapter 6: Applications. Introduction Systems of Rigid Bodies Trajectory Prescribed Path Control Electrical Networks DAE's Arising from the Method of Lines Bibliography Chapter 7: The DAE Home Page Introduction Theoretical Advances Numerical Analysis Advancements Software Tools for DAE-Solving Environments The DASSL Family Bibliography Index.

'[This book] is indisputably the best existing book on DAEs. It has structured the most important results on solvability properties, numerical methods, and software for DAEs. It is well written and describes difficulties with DAEs in a comprehensible way. It does not require any prior knowledge of the subject by the reader. The book is recommended to anyone who wants an introduction to DAEs. It is also a book that everyone who performs reseach on DAEs should have.' Anders Barrlund, OPTIMA