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© 1996

Solving Ordinary Differential Equations II

Stiff and Differential-Algebraic Problems

Book

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 14)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Stiff Problems — One-Step Methods

    1. Front Matter
      Pages 1-1
    2. Ernst Hairer, Gerhard Wanner
      Pages 2-14
    3. Ernst Hairer, Gerhard Wanner
      Pages 15-39
    4. Ernst Hairer, Gerhard Wanner
      Pages 40-50
    5. Ernst Hairer, Gerhard Wanner
      Pages 51-70
    6. Ernst Hairer, Gerhard Wanner
      Pages 71-90
    7. Ernst Hairer, Gerhard Wanner
      Pages 91-101
    8. Ernst Hairer, Gerhard Wanner
      Pages 102-117
    9. Ernst Hairer, Gerhard Wanner
      Pages 118-130
    10. Ernst Hairer, Gerhard Wanner
      Pages 131-142
    11. Ernst Hairer, Gerhard Wanner
      Pages 143-166
    12. Ernst Hairer, Gerhard Wanner
      Pages 167-179
    13. Ernst Hairer, Gerhard Wanner
      Pages 180-200
    14. Ernst Hairer, Gerhard Wanner
      Pages 201-214
    15. Ernst Hairer, Gerhard Wanner
      Pages 215-224
    16. Ernst Hairer, Gerhard Wanner
      Pages 225-238
  3. Multistep Methods for Stiff Problems

    1. Front Matter
      Pages 239-239
    2. Ernst Hairer, Gerhard Wanner
      Pages 240-249
    3. Ernst Hairer, Gerhard Wanner
      Pages 250-260

About this book

Introduction

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.

Keywords

Differential-algebraic systems Differentialgeichung Numerical analysis Numerik Ordinary differential equations Radiologieinformationssystem Runge-Kutta methods biology calculus control engineering multistep methods

Authors and affiliations

  1. 1.Section de Mathématiques, C.P. 240Université de GenèveGenève 24Switzerland

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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)