Hardcover ISBN:  9783985470167 
Product Code:  EMSTEXT/28 
List Price:  $89.00 
AMS Member Price:  $71.20 
Hardcover ISBN:  9783985470167 
Product Code:  EMSTEXT/28 
List Price:  $89.00 
AMS Member Price:  $71.20 

Book DetailsEMS Textbooks in MathematicsVolume: 28; 2024; 538 ppMSC: Primary 34; 65
Differentialalgebraic 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 differentialalgebraic 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 differentialalgebraic operators, generalized solutions, differential equations on manifolds, and differentialalgebraic equations with symmetries complement the theoretical treatment of initial value problems.
Two major classes of numerical methods for differentialalgebraic 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 differentialalgebraic equations. The analysis and numerical solution of boundary value problems for differentialalgebraic equations is presented, including multiple shooting and collocation methods. A chapter on further selected topics dealing with overdetermined consistent systems, root finding, path following, 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 selfstudy.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
ReadershipGraduate students and researchers in mathematics, engineering and sciences, as well as practitioners in industry interested in the theory and numerical solution of differentialalgebraic equations.

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Differentialalgebraic 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 differentialalgebraic 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 differentialalgebraic operators, generalized solutions, differential equations on manifolds, and differentialalgebraic equations with symmetries complement the theoretical treatment of initial value problems.
Two major classes of numerical methods for differentialalgebraic 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 differentialalgebraic equations. The analysis and numerical solution of boundary value problems for differentialalgebraic equations is presented, including multiple shooting and collocation methods. A chapter on further selected topics dealing with overdetermined consistent systems, root finding, path following, 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 selfstudy.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Graduate students and researchers in mathematics, engineering and sciences, as well as practitioners in industry interested in the theory and numerical solution of differentialalgebraic equations.