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  • Textbook
  • © 1985

Analysis of Approximation Methods for Differential and Integral Equations

Authors:

  1. H.-J. Reinhardt

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

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages N2-xi
    PDF

  2. Presentation of Numerical Methods

    1. Front Matter

      Pages 1-2
      PDF

    3. Projection Methods for Variational Equations

      • H.-J. Reinhardt
      Pages 20-50

  3. Convergence Theory

    1. Front Matter

      Pages 121-122
      PDF

    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
      PDF

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

    1. Front Matter

      Pages 266-267
      PDF

    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
    PDF
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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.
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Keywords

  • Analysis
  • Equations
  • Integral
  • Integral equation
  • numerical analysis
  • ordinary differential equation
  • partial differential equation
  • wave equation
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Authors and Affiliations

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

    H.-J. Reinhardt

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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

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Access via your institution

Buy it now

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

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