Applications Of Differential Algebraic Equations Examples And Benchmarks

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Applications Of Differential Algebraic Equations Examples And Benchmarks
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Author : Stephen Campbell
language : en
Publisher: Springer
Release Date : 2019-06-08
Applications Of Differential Algebraic Equations Examples And Benchmarks written by Stephen Campbell and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-08 with Mathematics categories.
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.
Differential Algebraic Equations A Projector Based Analysis
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Author : René Lamour
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-19
Differential Algebraic Equations A Projector Based Analysis written by René Lamour and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-19 with Mathematics categories.
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.
Progress In Differential Algebraic Equations Ii
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Author : Timo Reis
language : en
Publisher: Springer Nature
Release Date : 2020-10-10
Progress In Differential Algebraic Equations Ii written by Timo Reis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-10 with Mathematics categories.
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.
Numerical Solution Of Initial Value Problems In Differential Algebraic Equations
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Author : K. E. Brenan
language : en
Publisher: SIAM
Release Date : 1996-01-01
Numerical Solution Of Initial Value Problems In Differential Algebraic Equations written by K. E. Brenan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.
This book describes some of the places where differential-algebraic equations (DAE's) occur.
Progress In Industrial Mathematics Success Stories
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Author : Manuel Cruz
language : en
Publisher: Springer Nature
Release Date : 2021-03-19
Progress In Industrial Mathematics Success Stories written by Manuel Cruz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-19 with Mathematics categories.
This book presents a panorama about the recent progress of industrial mathematics from the point of view of both industrials and researchers. The chapters correspond to a selection of the contributions presented in the "Industry Day" and in the Minisymposium "EU - MATHS - IN: Success Stories of Applications of Mathematics to Industry" organized in the framework of the International Conference ICIAM 2019 held in Valencia (Spain) on July 15-19, 2019. In the Industry Day, included for the first time in this series of Conferences, representatives of companies from different countries and several sectors presented their view about the benefits regarding the usage of mathematical tools and/or collaboration with mathematicians. The contributions of this special session were addressed to industry people. Minisymposium contributions detailed some collaborations between mathematicians and industrials that led to real benefits in several European companies. All the speakers were affiliated in some of the European National Networks that constitute the European Service Network of Mathematics for Industry and Innovation (EU-MATHS-IN).
Optimal Control Of Odes And Daes
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Author : Matthias Gerdts
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-11-06
Optimal Control Of Odes And Daes written by Matthias Gerdts and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-06 with Technology & Engineering categories.
Ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) are widely used to model control systems in engineering, natural sciences, and economy. Optimal control plays a central role in optimizing such systems and to operate them effi ciently and safely. The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ODEs and DAEs. An emphasis is placed on the interplay between the optimal control problem, which typically is defi ned and analyzed in a Banach space setting, and discretizations thereof, which lead to finite dimensional optimization problems. The theoretical parts of the book require some knowledge of functional analysis, the numerically oriented parts require knowledge from linear algebra and numerical analysis. Practical examples are provided throughout the book for illustration purposes. The book addresses primarily master and PhD students as well as researchers in applied mathematics, but also engineers or scientists with a good background in mathematics. The book serves as a reference in research and teaching and hopefully helps to advance the state-of-the-art in optimal control.
Mathematical Analysis And Simulation Of Field Models In Accelerator Circuits
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Author : Idoia Cortes Garcia
language : en
Publisher: Springer Nature
Release Date : 2021-01-04
Mathematical Analysis And Simulation Of Field Models In Accelerator Circuits written by Idoia Cortes Garcia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-04 with Technology & Engineering categories.
This book deals with the analysis and development of numerical methods for the time-domain analysis of multiphysical effects in superconducting circuits of particle accelerator magnets. An important challenge is the simulation of “quenching”, i.e. the transition of a material from the superconducting to the normally electrically conductive state. The book analyses complex mathematical structures and presents models to simulate such quenching events in the context of generalized circuit elements. Furthermore, it proposes efficient parallelized algorithms with guaranteed convergence properties for the simulation of multiphysical problems. Spanning from theoretical concepts to applied research, and featuring rigorous mathematical presentations on one side, as well as simplified explanations of many complex issues, on the other side, this book provides graduate students and researchers with a comprehensive introduction on the state of the art and a source of inspiration for future research. Moreover, the proposed concepts and methods can be extended to the simulation of multiphysical phenomena in different application contexts.
The Numerical Solution Of Differential Algebraic Systems By Runge Kutta Methods
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Author : Ernst Hairer
language : en
Publisher: Springer
Release Date : 2006-11-14
The Numerical Solution Of Differential Algebraic Systems By Runge Kutta Methods written by Ernst Hairer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.
German Success Stories In Industrial Mathematics
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Author : Hans Georg Bock
language : en
Publisher: Springer Nature
Release Date : 2022-03-12
German Success Stories In Industrial Mathematics written by Hans Georg Bock and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-12 with Computers categories.
This book should illustrate the impact of collaborations between mathematics and industry. It is both an initiative of and coordinated by the German Committee for Mathematical Modeling, Simulation and Optimization (KoMSO). This publication aims at comparing the state of the art at the intersection of mathematics and industry, as well as the demands for future development of science and technology in Germany and beyond. Each contribution addresses the importance of mathematics in innovation by means of introducing a successful cooperation with an industrial partner in order to display the wide range of industrial sectors where the use of mathematics is the crucial factor for success, but also show the variety of mathematical areas involved in these activities. The success stories introduced in this volume will be supplemented by appropriate illustrations. It is the goal of this publication to highlight cooperation between mathematics and industry as a two-way technology and knowledge transfer, providing industry with solutions and mathematics with new research topics and inspiring new methodologies.
Data Driven Modeling And Optimization In Fluid Dynamics From Physics Based To Machine Learning Approaches
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Author : Michel Bergmann
language : en
Publisher: Frontiers Media SA
Release Date : 2023-01-05
Data Driven Modeling And Optimization In Fluid Dynamics From Physics Based To Machine Learning Approaches written by Michel Bergmann and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-05 with Science categories.