Analysis of Approximation Methods for Differential and Integral Equations

  • H.-J. Reinhardt
Book

Part of the Applied Mathematical Sciences book series (AMS, volume 57)

Table of contents

  1. Front Matter
    Pages N2-xi
  2. Presentation of Numerical Methods

  3. Convergence Theory

    1. Front Matter
      Pages 121-122
    2. H.-J. Reinhardt
      Pages 181-206
  4. Convergence Analysis for Approximate Solutions to Boundary-Value Problems and Integral Equations

  5. Inverse Stability, Consistency and Convergence for Initial Value Problems in Partial Differential Equations

  6. Back Matter
    Pages 385-399

About this book

Introduction

This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite­ difference methods and of projection methods for approximating their variational formulations.

Keywords

Analysis Equations Integral Integral equation numerical analysis ordinary differential equation partial differential equation wave equation

Authors and affiliations

  • H.-J. Reinhardt
    • 1
  1. 1.Fachbereich MathematikJohann-Wolfgang-Goethe-Universität6000 Frankfurt MainFederal Republic of Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1080-1
  • Copyright Information Springer-Verlag New York 1985
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96214-6
  • Online ISBN 978-1-4612-1080-1
  • Series Print ISSN 0066-5452
  • About this book
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