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The Concept of Stability in Numerical Mathematics

  • Wolfgang Hackbusch

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 45)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Wolfgang Hackbusch
    Pages 1-2
  3. Wolfgang Hackbusch
    Pages 3-15
  4. Wolfgang Hackbusch
    Pages 17-45
  5. Wolfgang Hackbusch
    Pages 47-62
  6. Wolfgang Hackbusch
    Pages 63-92
  7. Wolfgang Hackbusch
    Pages 93-138
  8. Wolfgang Hackbusch
    Pages 139-166
  9. Wolfgang Hackbusch
    Pages 167-184
  10. Back Matter
    Pages 185-188

About this book

Introduction

In this book, the author compares the meaning of stability in different subfields of numerical mathematics.

 Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations.

In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.

 

Keywords

differential equations integral equations interpolation quadature stability

Authors and affiliations

  • Wolfgang Hackbusch
    • 1
  1. 1.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-39386-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-39385-3
  • Online ISBN 978-3-642-39386-0
  • Series Print ISSN 0179-3632
  • Buy this book on publisher's site
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