Solving Ordinary Differential Equations II
Stiff and Differential-Algebraic Problems
Authors: Hairer, Ernst, Wanner, Gerhard
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- About this book
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The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). There is a chapter on one-step and extrapolation methods for stiff problems, another on multistep methods and general linear methods for stiff problems, a third on the treatment of singular perturbation problems, and a last one on differential-algebraic problems with applications to constrained mechanical systems. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g. in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented.
Ernst Hairer and Gerhard Wanner were jointly awarded the 2003 Peter Henrici Prize at ICIAM 2003 in Sydney, Australia.
- Reviews
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From the reviews of the second edition:
This is a superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text." Mathematics Today
“This volume, on nonstiff equations, is the second of a two-volume set. This second volume treats stiff differential equations and differential-algebraic equations. … This book is highly recommended as a text for courses in numerical methods for ordinary differential equations and as a reference for the worker. It should be in every library, both academic and industrial.” (Teodora-Liliana Rădulescu, Zentralblatt MATH, Vol. 1192, 2010)
- Table of contents (38 chapters)
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Examples of Stiff Equations
Pages 2-14
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Stability Analysis for Explicit RK Methods
Pages 15-39
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Stability Function of Implicit RK-Methods
Pages 40-50
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Order Stars
Pages 51-70
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Construction of Implicit Runge-Kutta Methods
Pages 71-90
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Table of contents (38 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Solving Ordinary Differential Equations II
- Book Subtitle
- Stiff and Differential-Algebraic Problems
- Authors
-
- Ernst Hairer
- Gerhard Wanner
- Series Title
- Springer Series in Computational Mathematics
- Series Volume
- 14
- Copyright
- 1996
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-642-05221-7
- DOI
- 10.1007/978-3-642-05221-7
- Hardcover ISBN
- 978-3-540-60452-5
- Softcover ISBN
- 978-3-642-05220-0
- Series ISSN
- 0179-3632
- Edition Number
- 2
- Number of Pages
- XV, 614
- Topics
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