EMS Textbooks in Mathematics 2006; 392 pp; hardcover Volume: 2 ISBN10: 3037190175 ISBN13: 9783037190173 List Price: US$68 Member Price: US$54.40 Order Code: EMSTEXT/2
 Differentialalgebraic equations are a widely accepted tool for the modeling and simulation of constrained dynamical systems in numerous applications, such as mechanical multibody systems, electrical circuit simulation, chemical engineering, control theory, fluid dynamics and many others. This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differentialalgebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, generalized inverses of differentialalgebraic operators, generalized solutions, and differential equations on manifolds complement the theoretical treatment of initial value problems. Two major classes of numerical methods for differentialalgebraic equations (RungeKutta and BDF methods) are discussed and analyzed with respect to convergence and order. A chapter is devoted to index reduction methods that allow the numerical treatment of general differentialalgebraic equations. The analysis and numerical solution of boundary value problems for differentialalgebraic equations is presented, including multiple shooting and collocation methods. A survey of current software packages for differentialalgebraic equations completes the text. The book is addressed to graduate students and researchers in mathematics, engineering and sciences, as well as practitioners in industry. A prerequisite is a standard course on the numerical solution of ordinary differential equations. Numerous examples and exercises make the book suitable as a course textbook or for selfstudy. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in differential equations. Table of Contents I. Analysis of differentialalgebraic equations  Introduction
 Linear differentialalgebraic equations with constant coefficients
 Linear differentialalgebraic equations with variable coefficients
 Nonlinear differentialalgebraic equations
II. Numerical solution of differentialalgebraic equations  Numerical methods for strangenessfree problems
 Numerical methods for index reduction
 Boundary value problems
 Software for the numerical solution of differentialalgebraic equations
 Final remarks
 Bibliography
 Index
