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Differential-algebraic equations. Analysis and numerical solution. (English) Zbl 1095.34004
Zürich: European Mathematical Society Publishing House (ISBN 3-03719-017-5/hbk). viii, 377 p. EUR 58.00 (2006).

The textbook is devoted to a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations (implicit differential equations, differential-algebraic systems, algebro-differential systems, descriptor systems, singular systems) that are a widely accepted tool for 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.

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 differential-algebraic operators, generalized solutions, and differential equations on manifolds complement the theoretical treatment of initial value problems. Two major classes of numerical methods for differential-algebraic equations (Runge-Kutta 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 differential-algebraic equations. The analysis and numerical solution of boundary value problems for differential-algebraic equations is presented, including multiple shooting and collocation methods. A survey of current software packages for differential-algebraic 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 self-study.


MSC:
34A09Implicit equations, differential-algebraic equations
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
34B15Nonlinear boundary value problems for ODE
65L80Numerical methods for differential-algebraic equations
65L06Multistep, Runge-Kutta, and extrapolation methods
65-01Textbooks (numerical analysis)
34-01Textbooks (ordinary differential equations)