Differential-Algebraic Equations: Analysis and Numerical Solution (EMS Textbooks in Mathematics) by Peter Kunkel and Volker Mehrmann (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This seems one of the most complete and realistic books on DAE but I still miss more applied exerises specialty to those related with chemical engineering, good theory book but could better with more exercises and maybe a cd with exercises in matlab or others softwares

⭐This book is used as the basic text in a graduate seminar onDAE’s. So far the participants find this book very useful.It is highly readable and meets the need of both basic and advancedstudy of DAE’s covering both theoretical and numerical techniques forsolving DAE’s with examples from control problems. There are exercisesto test the readers’ knowledge; these exercises are not difficult but very helpful for the understanding of the material.Compared with other texts this book includes more recent resultsin DAE. This book is highly recommended.

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