Solving Ordinary Differential Equations I

Nonstiff Problems

  • Ernst Hairer
  • Syvert Paul Nørsett
  • Gerhard Wanner

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 8)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ernst Hairer, Syvert Paul Nørsett, Gerhard Wanner
    Pages 1-125
  3. Ernst Hairer, Syvert Paul Nørsett, Gerhard Wanner
    Pages 127-301
  4. Ernst Hairer, Syvert Paul Nørsett, Gerhard Wanner
    Pages 303-432
  5. Back Matter
    Pages 433-482

About this book

Introduction

"So far as I remember, I have never seen an Author's Pre­ face which had any purpose but one - to furnish reasons for the publication of the Book. " (Mark Twain) "Gauss' dictum, "when a building is completed no one should be able to see any trace of the scaffolding," is often used by mathematicians as an excuse for neglecting the motivation behind their own work and the history of their field. For­ tunately, the opposite sentiment is gaining strength, and numerous asides in this Essay show to which side go my sympathies. " (B. B. Mandelbrot, 1982) 'This gives us a good occasion to work out most of the book until the next year. " (the Authors in a letter, dated c. kt. 29, 1980, to Springer Verlag) There are two volumes, one on non-stiff equations, now finished, the second on stiff equations, in preparation. The first volume has three chapters, one on classical mathematical theory, one on Runge­ Kutta and extrapolation methods, and one on multistep methods. There is an Appendix containing some Fortran codes which we have written for our numerical examples. Each chapter is divided into sections. Numbers of formulas, theorems, tables and figures are consecutive in each section and indi­ cate, in addition, the section number, but not the chapter number. Cross references to other chapters are rare and are stated explicitly. The end of a proof is denoted by "QED" (quod erat demonstrandum).

Keywords

Gewöhnliche Differentialgleichungen Mehrschrittverfahren Multistep Methods Numerical Analysis Numerische Analysis Ordinary Differential Equations Runge-Kutta-Methoden Runge-Kutta-Methods differential equation ordinary differential equation

Authors and affiliations

  • Ernst Hairer
    • 1
  • Syvert Paul Nørsett
    • 2
  • Gerhard Wanner
    • 1
  1. 1.Section de MathématiquesUniversité de GenèveGenève 24Switzerland
  2. 2.Department of Numerical MathematicsUniversity of Trondheim, NTHTrondheimNorway

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-12607-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-12609-7
  • Online ISBN 978-3-662-12607-3
  • Series Print ISSN 0179-3632
  • About this book