Ebook: Differential-Algebraic Equations: A Projector Based Analysis

Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980s, no more than about three decades ago. In this relatively short time, DAEs have become a widely acknowledged tool to model processes subjected to constraints, in order to simulate and to control processes in various application fields such as network simulation, chemical kinematics, mechanical engineering, system biology.
DAEs and their more abstract versions in infinite-dimensional spaces comprise a great potential for future mathematical modeling of complex coupled processes.
The purpose of the book is to expose the impressive complexity of general DAEs from an analytical point of view, to describe the state of the art as well as open problems and so to motivate further research to this versatile, extra-ordinary topic from a broader mathematical perspective.
The book elaborates a new general structural analysis capturing linear and nonlinear DAEs in a hierarchical way. The DAE structure is exposed by means of special projector functions. Numerical integration issues and computational aspects are treated also in this context.

---

Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980s, no more than about three decades ago. In this relatively short time, DAEs have become a widely acknowledged tool to model processes subjected to certain constraints in order to simulate and to control processes in various application fields such as network simulation, chemical kinematics, mechanical engineering and systems biology.
DAEs and their more abstract versions in infinite dimensional spaces comprise a great potential for the future mathematical modeling of complex coupled processes.
The purpose of the book is to expose the impressive complexity of general DAEs from an analytical point of view, to describe the state of the art as well as open problems and in so doing to motivate further research of this versatile, extraordinary topic from a broader mathematical perspective.
The book elaborates on a new general, structural analysis capturing linear and nonlinear DAEs in a hierarchical way. The DAE structure is exposed by means of special projector functions. Some issues on numerical integration and computational aspects are also treated in this context.

---

Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980s, no more than about three decades ago. In this relatively short time, DAEs have become a widely acknowledged tool to model processes subjected to certain constraints in order to simulate and to control processes in various application fields such as network simulation, chemical kinematics, mechanical engineering and systems biology.
DAEs and their more abstract versions in infinite dimensional spaces comprise a great potential for the future mathematical modeling of complex coupled processes.
The purpose of the book is to expose the impressive complexity of general DAEs from an analytical point of view, to describe the state of the art as well as open problems and in so doing to motivate further research of this versatile, extraordinary topic from a broader mathematical perspective.
The book elaborates on a new general, structural analysis capturing linear and nonlinear DAEs in a hierarchical way. The DAE structure is exposed by means of special projector functions. Some issues on numerical integration and computational aspects are also treated in this context.
Content:
Front Matter....Pages I-XXVII
Front Matter....Pages 1-2
Linear constant coefficient DAEs....Pages 3-56
Linear DAEs with variable coefficients....Pages 57-181
Nonlinear DAEs....Pages 183-314
Front Matter....Pages 315-316
Analysis....Pages 317-337
Numerical integration....Pages 339-373
Stability issues....Pages 375-395
Front Matter....Pages 397-398
Computational linear algebra aspects....Pages 399-417
Aspects of the numerical treatment of higher index DAEs....Pages 419-438
Front Matter....Pages 439-440
Quasi-regular DAEs....Pages 441-476
Nonregular DAEs....Pages 477-503
Minimization with constraints described by DAEs....Pages 505-538
Abstract differential-algebraic equations....Pages 539-580
Back Matter....Pages 581-649

---

Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980s, no more than about three decades ago. In this relatively short time, DAEs have become a widely acknowledged tool to model processes subjected to certain constraints in order to simulate and to control processes in various application fields such as network simulation, chemical kinematics, mechanical engineering and systems biology.
DAEs and their more abstract versions in infinite dimensional spaces comprise a great potential for the future mathematical modeling of complex coupled processes.
The purpose of the book is to expose the impressive complexity of general DAEs from an analytical point of view, to describe the state of the art as well as open problems and in so doing to motivate further research of this versatile, extraordinary topic from a broader mathematical perspective.
The book elaborates on a new general, structural analysis capturing linear and nonlinear DAEs in a hierarchical way. The DAE structure is exposed by means of special projector functions. Some issues on numerical integration and computational aspects are also treated in this context.
Content:
Front Matter....Pages I-XXVII
Front Matter....Pages 1-2
Linear constant coefficient DAEs....Pages 3-56
Linear DAEs with variable coefficients....Pages 57-181
Nonlinear DAEs....Pages 183-314
Front Matter....Pages 315-316
Analysis....Pages 317-337
Numerical integration....Pages 339-373
Stability issues....Pages 375-395
Front Matter....Pages 397-398
Computational linear algebra aspects....Pages 399-417
Aspects of the numerical treatment of higher index DAEs....Pages 419-438
Front Matter....Pages 439-440
Quasi-regular DAEs....Pages 441-476
Nonregular DAEs....Pages 477-503
Minimization with constraints described by DAEs....Pages 505-538
Abstract differential-algebraic equations....Pages 539-580
Back Matter....Pages 581-649
....