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Well-Posedness of Parabolic Difference Equations

  • Book
  • © 1994

Overview

Authors:
  1. A. Ashyralyev

    1. Department of Mathematical Analysis, The Turkmen State University, Ashgabat, Turkmenistan

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    You can also search for this author in PubMed   Google Scholar

  2. P. E. Sobolevskii

    1. Institute of Mathematics, The Hebrew University, Jerusalem, Israel

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Operator Theory: Advances and Applications (OT, volume 69)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xiv
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  2. The Abstract Cauchy Problem

    • A. Ashyralyev, P. E. Sobolevskii
    Pages 1-69

  3. The Rothe Difference Scheme

    • A. Ashyralyev, P. E. Sobolevskii
    Pages 71-156

  4. Padé Difference Schemes

    • A. Ashyralyev, P. E. Sobolevskii
    Pages 157-240

  5. Difference Schemes for Parabolic Equations

    • A. Ashyralyev, P. E. Sobolevskii
    Pages 241-326

  6. Back Matter

    Pages 327-353
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Keywords

About this book

A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.

Authors and Affiliations

  • Department of Mathematical Analysis, The Turkmen State University, Ashgabat, Turkmenistan

    A. Ashyralyev

  • Institute of Mathematics, The Hebrew University, Jerusalem, Israel

    P. E. Sobolevskii

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