Springer Series in Computational Mathematics

Solving Ordinary Differential Equations II

Stiff and Differential-Algebraic Problems

Authors: Hairer, Ernst, Wanner, Gerhard

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  • ISBN 978-3-642-05221-7
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About this book

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

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)

  • Examples of Stiff Equations

    Hairer, Ernst (et al.)

    Pages 2-14

  • Stability Analysis for Explicit RK Methods

    Hairer, Ernst (et al.)

    Pages 15-39

  • Stability Function of Implicit RK-Methods

    Hairer, Ernst (et al.)

    Pages 40-50

  • Order Stars

    Hairer, Ernst (et al.)

    Pages 51-70

  • Construction of Implicit Runge-Kutta Methods

    Hairer, Ernst (et al.)

    Pages 71-90

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-3-642-05221-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $219.00
price for USA
  • ISBN 978-3-540-60452-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-3-642-05220-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Solving Ordinary Differential Equations II
Book Subtitle
Stiff and Differential-Algebraic Problems
Authors
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