Skip to main content
SpringerLink
Log in

Numerical Methods for Singularly Perturbed Differential Equations

Convection-Diffusion and Flow Problems

  • Book
  • © 1996

Overview

Authors:
  1. Hans-Görg Roos

    1. Institut für Numerische Mathematik, Technische Universität Dresden, Dresden, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Martin Stynes

    1. Department of Mathematics, University College Cork, Cork, Ireland

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Lutz Tobiska

    1. Institut für Analysis und Numerik, Otto-von-Guericke Universität Magdeburg, Magdeburg, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 24)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (4 chapters)

  1. Front Matter

    Pages I-XVI
    Download chapter PDF

  2. Ordinary Differential Equations

    • Hans-Görg Roos, Martin Stynes, Lutz Tobiska
    Pages 1-103

  3. Parabolic Initial-Boundary Value Problems in One Space Dimension

    • Hans-Görg Roos, Martin Stynes, Lutz Tobiska
    Pages 105-171

  4. Elliptic Boundary Value Problems

    • Hans-Görg Roos, Martin Stynes, Lutz Tobiska
    Pages 173-278

  5. Incompressible Navier-Stokes Equations

    • Hans-Görg Roos, Martin Stynes, Lutz Tobiska
    Pages 279-320

  6. Back Matter

    Pages 321-351
    Download chapter PDF
Back to top

Keywords

About this book

The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex­ pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex­ pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa­ tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.

Authors and Affiliations

  • Institut für Numerische Mathematik, Technische Universität Dresden, Dresden, Germany

    Hans-Görg Roos

  • Department of Mathematics, University College Cork, Cork, Ireland

    Martin Stynes

  • Institut für Analysis und Numerik, Otto-von-Guericke Universität Magdeburg, Magdeburg, Germany

    Lutz Tobiska

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation