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Solving Ordinary Differential Equations II

Stiff and Differential-Algebraic Problems

  • Ernst Hairer
  • Gerhard Wanner

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

Table of contents

  1. Front Matter
    Pages I-XV
  2. Ernst Hairer, Gerhard Wanner
    Pages 1-254
  3. Ernst Hairer, Gerhard Wanner
    Pages 255-398
  4. Ernst Hairer, Gerhard Wanner
    Pages 399-545
  5. Back Matter
    Pages 547-604

About this book

Introduction

"Whatever regrets may be, we have done our best." (Sir Ernest Shackleton, turning back on 9 January 1909 at 88°23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential alge­ braic equations. It contains three chapters: Chapter IV on one-step (Runge­ Kutta) methods for stiff problems, Chapter Von multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretieal nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered consecutively in each section and indicate, in addition, the section num­ ber. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.

Keywords

Differential-algebraic systems Differentialgeichung Numerik Ordinary differential equations Runge-Kutta methods differential equation multistep methods numerical analysis numerics ordinary differential equation

Authors and affiliations

  • Ernst Hairer
    • 1
  • Gerhard Wanner
    • 1
  1. 1.Section de MathématiquesUniversité de GenèveGenève 24Switzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-09947-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-09949-0
  • Online ISBN 978-3-662-09947-6
  • Series Print ISSN 0179-3632
  • Buy this book on publisher's site