Differential-Algebraic Equations

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 other areas.

In the second edition of this textbook a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations is provided. 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, optimal control, stability theory, generalized inverses of differential-algebraic operators, generalized solutions, differential equations on manifolds, and differential-algebraic equations with symmetries 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 chapter on further selected topics dealing with overdetermined consistent systems, root finding, pathfollowing, hybrid systems, and dissipative Hamiltonian systems completes the book.

A prerequisite for the reader is the standard course on the theory and numerical solution of ordinary differential equations. Numerous examples and exercises make the book suitable as a course textbook or for self-study.

For the first edition of this book, please click here.