Skip to main content
SpringerLink
Log in
Book cover

Analysis of Approximation Methods for Differential and Integral Equations

  • Textbook
  • © 1985

Overview

Authors:
  1. H.-J. Reinhardt

    1. Fachbereich Mathematik, Johann-Wolfgang-Goethe-Universität, 6000 Frankfurt Main, Federal Republic of Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (13 chapters)

  1. Front Matter

    Pages N2-xi
    Download chapter PDF

  3. Convergence Theory

    1. Front Matter

      Pages 121-122
      Download chapter PDF

    2. The Concepts of Discrete Convergence and Discrete Approximations

      • H.-J. Reinhardt
      Pages 123-151

    3. Discrete Convergence of Mappings and Solutions of Equations

      • H.-J. Reinhardt
      Pages 152-180

    4. Compactness Criteria for Discrete Convergence

      • H.-J. Reinhardt
      Pages 181-206

  4. Convergence Analysis for Approximate Solutions to Boundary-Value Problems and Integral Equations

    1. Front Matter

      Pages 207-208
      Download chapter PDF

    2. Convergence of Finite-Difference Methods for Boundary-Value Problems

      • H.-J. Reinhardt
      Pages 209-235

    3. Biconvergence for Projection Methods via Variational Principles

      • H.-J. Reinhardt
      Pages 236-250

    4. Convergence of Perturbations of Integral Equations of the Second Kind

      • H.-J. Reinhardt
      Pages 251-265

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

    1. Front Matter

      Pages 266-267
      Download chapter PDF

    2. Inverse Stability and Convergence for General Discrete-Time Approximations of Linear and Nonlinear Initial Value Problems

      • H.-J. Reinhardt
      Pages 268-305

    3. Special Criteria for Inverse Stability

      • H.-J. Reinhardt
      Pages 306-353

    4. Convergence Analysis of Special Methods

      • H.-J. Reinhardt
      Pages 354-384

  6. Back Matter

    Pages 385-399
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Fachbereich Mathematik, Johann-Wolfgang-Goethe-Universität, 6000 Frankfurt Main, Federal Republic of Germany

    H.-J. Reinhardt

Bibliographic Information

  • Book Title: Analysis of Approximation Methods for Differential and Integral Equations

  • Authors: H.-J. Reinhardt

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-1080-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1985

  • Softcover ISBN: 978-0-387-96214-6Published: 07 October 1985

  • eBook ISBN: 978-1-4612-1080-1Published: 06 December 2012

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: 398

  • Topics: Numerical Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation