Progress in Differential-Algebraic Equations

Progress in Differential-Algebraic Equations
Author: Sebastian Schöps
Publisher: Springer
Total Pages: 211
Release: 2014-11-13
Genre: Mathematics
ISBN: 3662449269

This book contains the proceedings of the 8th Workshop on Coupled Descriptor Systems held March 2013 in the Castle of Eringerfeld, Geseke in the neighborhood of Paderborn, Germany. It examines the wide range of current research topics in descriptor systems, including mathematical modeling, index analysis, wellposedness of problems, stiffness and different time-scales, cosimulation and splitting methods and convergence analysis. In addition, the book also presents applications from the automotive and circuit industries that show that descriptor systems provide challenging problems from the point of view of both theory and practice. The book contains nine papers and is organized into three parts: control, simulation, and model order reduction. It will serve as an ideal resource for applied mathematicians and engineers, in particular those from mechanics and electromagnetics, who work with coupled differential equations.

Progress in Differential-Algebraic Equations II

Progress in Differential-Algebraic Equations II
Author: Timo Reis
Publisher: Springer Nature
Total Pages: 486
Release: 2020-10-10
Genre: Mathematics
ISBN: 3030539059

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

Numerical Solution of Initial-value Problems in Differential-algebraic Equations
Author: K. E. Brenan
Publisher: SIAM
Total Pages: 268
Release: 1996-01-01
Genre: Mathematics
ISBN: 9781611971224

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.

Recent Advances in Differential Equations and Applications

Recent Advances in Differential Equations and Applications
Author: Juan Luis García Guirao
Publisher: Springer
Total Pages: 250
Release: 2019-01-04
Genre: Mathematics
ISBN: 3030003418

This work gathers a selection of outstanding papers presented at the 25th Conference on Differential Equations and Applications / 15th Conference on Applied Mathematics, held in Cartagena, Spain, in June 2017. It supports further research into both ordinary and partial differential equations, numerical analysis, dynamical systems, control and optimization, trending topics in numerical linear algebra, and the applications of mathematics to industry. The book includes 14 peer-reviewed contributions and mainly addresses researchers interested in the applications of mathematics, especially in science and engineering. It will also greatly benefit PhD students in applied mathematics, engineering and physics.

Solving Ordinary Differential Equations II

Solving Ordinary Differential Equations II
Author: Ernst Hairer
Publisher: Springer Science & Business Media
Total Pages: 615
Release: 2013-03-14
Genre: Mathematics
ISBN: 3662099470

"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.

Model Order Reduction: Theory, Research Aspects and Applications

Model Order Reduction: Theory, Research Aspects and Applications
Author: Wilhelmus H. Schilders
Publisher: Springer Science & Business Media
Total Pages: 471
Release: 2008-08-27
Genre: Mathematics
ISBN: 3540788417

The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.

Finite Difference Methods for Ordinary and Partial Differential Equations

Finite Difference Methods for Ordinary and Partial Differential Equations
Author: Randall J. LeVeque
Publisher: SIAM
Total Pages: 356
Release: 2007-01-01
Genre: Mathematics
ISBN: 9780898717839

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

De Rham Cohomology of Differential Modules on Algebraic Varieties

De Rham Cohomology of Differential Modules on Algebraic Varieties
Author: Yves André
Publisher: Birkhäuser
Total Pages: 223
Release: 2012-12-06
Genre: Mathematics
ISBN: 3034883366

"...A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong...This is a nicely-written book [that] studies algebraic differential modules in several variables." --Mathematical Reviews

Computational Flexible Multibody Dynamics

Computational Flexible Multibody Dynamics
Author: Bernd Simeon
Publisher: Springer Science & Business Media
Total Pages: 254
Release: 2013-06-14
Genre: Mathematics
ISBN: 3642351581

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.