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Differential Algebraic Equations
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Book Synopsis Differential-algebraic Equations by : Peter Kunkel
Download or read book Differential-algebraic Equations written by Peter Kunkel and published by European Mathematical Society. This book was released on 2006 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Differential-Algebraic Equations: A Projector Based Analysis by : René Lamour
Download or read book Differential-Algebraic Equations: A Projector Based Analysis written by René Lamour and published by Springer Science & Business Media. This book was released on 2013-01-19 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations by : Uri M. Ascher
Download or read book Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations written by Uri M. Ascher and published by SIAM. This book was released on 1998-08-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains all the material necessary for a course on the numerical solution of differential equations.
Book Synopsis Numerical Solution of Initial-value Problems in Differential-algebraic Equations by : K. E. Brenan
Download or read book Numerical Solution of Initial-value Problems in Differential-algebraic Equations written by K. E. Brenan and published by SIAM. This book was released on 1996-01-01 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. This classic edition, originally published in 1989, is the only general DAE book available. It not only develops guidelines for choosing different numerical methods, it is the first book to discuss DAE codes, including the popular DASSL code. An extensive discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAE's. New to this edition is a chapter that brings the discussion of DAE software up to date. The objective of this monograph is to advance and consolidate the existing research results for the numerical solution of DAE's. The authors present results on the analysis of numerical methods, and also show how these results are relevant for the solution of problems from applications. They develop guidelines for problem formulation and effective use of the available mathematical software and provide extensive references for further study.
Book Synopsis The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods by : Ernst Hairer
Download or read book The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods written by Ernst Hairer and published by Springer. This book was released on 2006-11-14 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications.
Book Synopsis Applications of Differential-Algebraic Equations: Examples and Benchmarks by : Stephen Campbell
Download or read book Applications of Differential-Algebraic Equations: Examples and Benchmarks written by Stephen Campbell and published by Springer. This book was released on 2019-06-08 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Surveys in Differential-Algebraic Equations III by : Achim Ilchmann
Download or read book Surveys in Differential-Algebraic Equations III written by Achim Ilchmann and published by Springer. This book was released on 2015-10-29 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Control and Optimization with Differential-Algebraic Constraints by : Lorenz T. Biegler
Download or read book Control and Optimization with Differential-Algebraic Constraints written by Lorenz T. Biegler and published by SIAM. This book was released on 2012-11-01 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: A cutting-edge guide to modelling complex systems with differential-algebraic equations, suitable for applied mathematicians, engineers and computational scientists.
Book Synopsis Solving Ordinary Differential Equations II by : Ernst Hairer
Download or read book Solving Ordinary Differential Equations II written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Whatever regrets may be, we have done our best." (Sir Ernest Shackleton, turning back on 9 January 1909 at 88°23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential alge braic equations. It contains three chapters: Chapter IV on one-step (Runge Kutta) methods for stiff problems, Chapter Von multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretieal nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered consecutively in each section and indicate, in addition, the section num ber. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.
Book Synopsis Progress in Differential-Algebraic Equations II by : Timo Reis
Download or read book Progress in Differential-Algebraic Equations II written by Timo Reis and published by Springer Nature. This book was released on 2020-10-10 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Pyomo – Optimization Modeling in Python by : William E. Hart
Download or read book Pyomo – Optimization Modeling in Python written by William E. Hart and published by Springer Science & Business Media. This book was released on 2012-02-15 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a complete and comprehensive reference/guide to Pyomo (Python Optimization Modeling Objects) for both beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, and practitioners. The text illustrates the breadth of the modeling and analysis capabilities that are supported by the software and support of complex real-world applications. Pyomo is an open source software package for formulating and solving large-scale optimization and operations research problems. The text begins with a tutorial on simple linear and integer programming models. A detailed reference of Pyomo's modeling components is illustrated with extensive examples, including a discussion of how to load data from data sources like spreadsheets and databases. Chapters describing advanced modeling capabilities for nonlinear and stochastic optimization are also included. The Pyomo software provides familiar modeling features within Python, a powerful dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parameters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can be used from a command-line interface and within Python's interactive command environment, which makes it easy to create Pyomo models, apply a variety of optimizers, and examine solutions. The software supports a different modeling approach than commercial AML (Algebraic Modeling Languages) tools, and is designed for flexibility, extensibility, portability, and maintainability but also maintains the central ideas in modern AMLs.
Book Synopsis Computational Flexible Multibody Dynamics by : Bernd Simeon
Download or read book Computational Flexible Multibody Dynamics written by Bernd Simeon and published by Springer Science & Business Media. This book was released on 2013-06-14 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph, written from a numerical analysis perspective, aims to provide a comprehensive treatment of both the mathematical framework and the numerical methods for flexible multibody dynamics. Not only is this field permanently and rapidly growing, with various applications in aerospace engineering, biomechanics, robotics, and vehicle analysis, its foundations can also be built on reasonably established mathematical models. Regarding actual computations, great strides have been made over the last two decades, as sophisticated software packages are now capable of simulating highly complex structures with rigid and deformable components. The approach used in this book should benefit graduate students and scientists working in computational mechanics and related disciplines as well as those interested in time-dependent partial differential equations and heterogeneous problems with multiple time scales. Additionally, a number of open issues at the frontiers of research are addressed by taking a differential-algebraic approach and extending it to the notion of transient saddle point problems.
Book Synopsis Solving Differential Equations in R by : Karline Soetaert
Download or read book Solving Differential Equations in R written by Karline Soetaert and published by Springer Science & Business Media. This book was released on 2012-06-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.
Book Synopsis Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory by : Peter Benner
Download or read book Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory written by Peter Benner and published by Springer. This book was released on 2015-05-09 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.
Book Synopsis Algebraic Analysis of Differential Equations by : T. Aoki
Download or read book Algebraic Analysis of Differential Equations written by T. Aoki and published by Springer Science & Business Media. This book was released on 2009-03-15 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics.
Book Synopsis Surveys in Differential-Algebraic Equations IV by : Achim Ilchmann
Download or read book Surveys in Differential-Algebraic Equations IV written by Achim Ilchmann and published by Springer. This book was released on 2017-03-08 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Solution of Ordinary Differential Equations by : Kendall Atkinson
Download or read book Numerical Solution of Ordinary Differential Equations written by Kendall Atkinson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.
