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Numerical solution of initial-value problems in differential-algebraic equations

Author: Kathryn Eleda Brenan; S L Campbell; Linda Ruth Petzold; Society for Industrial and Applied Mathematics.
Publisher: Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1996.
Series: Classics in applied mathematics, 14.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
(DLC) 95046482
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Kathryn Eleda Brenan; S L Campbell; Linda Ruth Petzold; Society for Industrial and Applied Mathematics.
ISBN: 9781611971224 1611971225
OCLC Number: 722473257
Notes: Title from title screen, viewed 04/05/2011.
"An unabridged, corrected republication of the work first published by North-Holland, New York, 1989"--Title page verso.
Description: 1 electronic text (x, 256 pages) : illustrations, digital file.
Contents: Preface --
Chapter 1. Introduction --
Chapter 2. Theory of DAE's --
Chapter 3. Multistep methods --
Chapter 4. One-step methods --
Chapter 5. Software and DAE's --
Chapter 6. Applications --
Chapter 7. The DAE home page --
Supplementary bibliography --
Index.
Series Title: Classics in applied mathematics, 14.
Responsibility: K.E. Brenan, S.L. Campbell, L.R. Petzold.
More information:

Abstract:

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.

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