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This book contains articles presented at the 9th Workshop on
Differential-Algebraic Equations held in Paderborn, Germany, from
17-20 March 2019. The workshop brought together more than 40
mathematicians and engineers from various fields, such as numerical
and functional analysis, control theory, mechanics and
electromagnetic field theory. The participants focussed on the
theoretical and numerical treatment of "descriptor" systems, i.e.,
differential-algebraic equations (DAEs). The book contains 14
contributions and is organized into four parts: mathematical
analysis, numerics and model order reduction, control as well as
applications. It is a useful resource for applied mathematicians
with interest in recent developments in the field of differential
algebraic equations but also for engineers, in particular those
interested in modelling of constraint mechanical systems, thermal
networks or electric circuits.
The present volume comprises survey articles on various fields of
Differential-Algebraic Equations (DAEs) which have widespread
applications in controlled dynamical systems, especially in
mechanical and electrical engineering and a strong relation to
(ordinary) differential equations. The individual chapters provide
reviews, presentations of the current state of research and new
concepts in - History of DAEs - DAE aspects of mechanical multibody
systems - Model reduction of DAEs - Observability for DAEs -
Numerical Analysis for DAEs The results are presented in an
accessible style, making this book suitable not only for active
researchers but also for graduate students (with a good knowledge
of the basic principles of DAEs) for self-study.
The present volume comprises survey articles on various fields of
Differential-Algebraic Equations (DAEs), which have widespread
applications in controlled dynamical systems, especially in
mechanical and electrical engineering and a strong relation to
(ordinary) differential equations. The individual chapters provide
reviews, presentations of the current state of research and new
concepts in - Flexibility of DAE formulations - Reachability
analysis and deterministic global optimization - Numerical linear
algebra methods - Boundary value problems The results are presented
in an accessible style, making this book suitable not only for
active researchers but also for graduate students (with a good
knowledge of the basic principles of DAEs) for self-study.
The present volume comprises survey articles on various fields of
Differential-Algebraic Equations (DAEs), which have widespread
applications in controlled dynamical systems, especially in
mechanical and electrical engineering and a strong relation to
(ordinary) differential equations. The individual chapters provide
reviews, presentations of the current state of research and new
concepts in - Observers for DAEs - DAEs in chemical processes -
Optimal control of DAEs - DAEs from a functional-analytic viewpoint
- Algebraic methods for DAEs The results are presented in an
accessible style, making this book suitable not only for active
researchers but also for graduate students (with a good knowledge
of the basic principles of DAEs) for self-study.
The need for a rigorous mathematical theory for
Differential-Algebraic Equations (DAEs) has its roots in the
widespread applications of controlled dynamical systems, especially
in mechanical and electrical engineering. Due to the strong
relation to (ordinary) differential equations, the literature for
DAEs mainly started out from introductory textbooks. As such, the
present monograph is new in the sense that it comprises survey
articles on various fields of DAEs, providing reviews,
presentations of the current state of research and new concepts in
- Controllability for linear DAEs - Port-Hamiltonian
differential-algebraic systems - Robustness of DAEs - Solution
concepts for DAEs - DAEs in circuit modeling. The results in the
individual chapters are presented in an accessible style, making
this book suitable not only for active researchers but also for
graduate students (with a good knowledge of the basic principles of
DAEs) for self-study.
This volume encompasses prototypical, innovative and emerging
examples and benchmarks of Differential-Algebraic Equations (DAEs)
and their applications, such as electrical networks, chemical
reactors, multibody systems, and multiphysics models, to name but a
few. Each article begins with an exposition of modelling,
explaining whether the model is prototypical and for which
applications it is used. This is followed by a mathematical
analysis, and if appropriate, a discussion of the numerical aspects
including simulation. Additionally, benchmark examples are included
throughout the text. Mathematicians, engineers, and other
scientists, working in both academia and industry either on
differential-algebraic equations and systems or on problems where
the tools and insight provided by differential-algebraic equations
could be useful, would find this book resourceful.
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