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9780898713534 Academic Inspection Copy

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

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Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAEs) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. The book develops guidelines for choosing different numerical methods, and discusses DAE codes, including the popular DASSL code. A discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAEs. New to this edition is a chapter that brings the discussion of DAE software up to date.
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
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