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

  • Ernst Hairer
    • 1
  • Gerhard Wanner
    • 1
  1. 1.Section de Mathématiques, C.P. 240Université de GenèveGenève 24Switzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-05221-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-05220-0
  • Online ISBN 978-3-642-05221-7
  • Series Print ISSN 0179-3632
  • About this book