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Differential-Algebraic Equations: Analysis and Numerical Solution
Peter Kunkel, University of Leipzig, Germany, and Volker Mehrmann, Technical University of Berlin, Germany
A publication of the European Mathematical Society.
EMS Textbooks in Mathematics
2006; 392 pp; hardcover
Volume: 2
ISBN-10: 3-03719-017-5
ISBN-13: 978-3-03719-017-3
List Price: US$68
Member Price: US$54.40
Order Code: EMSTEXT/2
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Differential-algebraic 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 differential-algebraic 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 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.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.


Graduate students and research mathematicians interested in differential equations.

Table of Contents

I. Analysis of differential-algebraic equations
  • Introduction
  • Linear differential-algebraic equations with constant coefficients
  • Linear differential-algebraic equations with variable coefficients
  • Nonlinear differential-algebraic equations
II. Numerical solution of differential-algebraic equations
  • Numerical methods for strangeness-free problems
  • Numerical methods for index reduction
  • Boundary value problems
  • Software for the numerical solution of differential-algebraic equations
  • Final remarks
  • Bibliography
  • Index
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