# Differential-algebraic Equations: Analysis and Numerical Solution

European Mathematical Society, 2006 - Mathematics - 377 pages
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.

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asalam o alikum
it is a very googd book on differential algebraic equation.i am also work on this equation.

### Contents

 Introduction 3 Linear differentialalgebraic equations with constant coefﬁcients 13 Linear differentialalgebraic equations with variable coefﬁcients 56 Nonlinear differentialalgebraic equations 151 Numerical methods for strangenessfree problems 217 Numerical methods for index reduction 273
 Boundary value problems 298 Software for the numerical solution of differentialalgebraic 352 Bibliography 359 Index 373 Copyright