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Method of Difference Potentials and Its Applications

  • Book
  • © 2002

Overview

Authors:
  1. Viktor S. Ryaben’kii

    1. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

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  • First English edition of a well-known Russian monograph.
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 30)

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Table of contents (23 chapters)

  1. Front Matter

    Pages I-XVIII
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  2. Introduction

    1. Introduction

      • Viktor S. Ryaben’kii
      Pages 1-32

  3. Justification of Algorithms of the Method of Difference Potentials for Calculating Numerical Solutions of Interior Boundary-Value Problems for the Laplace Equation

    1. Front Matter

      Pages 33-35
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    2. Preliminaries

      • Viktor S. Ryaben’kii
      Pages 37-52

    3. Differential and Difference Potentials

      • Viktor S. Ryaben’kii
      Pages 53-80

    4. Reduction of Boundary-Value Problems for the Laplace Equation to Boundary Equations of Calderón—Seeley Type

      • Viktor S. Ryaben’kii
      Pages 81-86

    5. Numerical Solution of Boundary-Value Problems

      • Viktor S. Ryaben’kii
      Pages 87-136

  4. General Constructions of Surface Potentials and Boundary Equations on the Basis of the Concept of a Clear Trace

    1. Front Matter

      Pages 137-139
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    2. Generalized Potentials and Boundary Equations with Projections for Differential Operators

      • Viktor S. Ryaben’kii
      Pages 141-158

    3. General Constructions of Potentials and Boundary Equations for Difference Operators

      • Viktor S. Ryaben’kii
      Pages 159-206

    4. Lazarev’s Results on the Algebraic Structure of the Set of Surface Potentials of a Linear Operator

      • Viktor S. Ryaben’kii
      Pages 207-212

  5. A General Scheme of the Method of Difference Potentials for the Numerical Solution of Differential and Difference Boundary-Value Problems of Mathematical Physics

    1. Front Matter

      Pages 213-215
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    2. A General Scheme of the Method of Difference Potentials for Differential Problems

      • Viktor S. Ryaben’kii
      Pages 217-272

    3. Illustrations of Constructions of the Method of Difference Potentials

      • Viktor S. Ryaben’kii
      Pages 273-290

    4. General Scheme of the Method of Difference Potentials for Solving Numerically the Difference Analogs of Differential Boundary-Value Problems

      • Viktor S. Ryaben’kii
      Pages 291-324

  6. Examples of MDP Algorithms for Solving Numerically Boundary-Value Problems of Mathematical Physics

    1. Front Matter

      Pages 325-327
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    2. The Tricomi Problem

      • Viktor S. Ryaben’kii
      Pages 329-340

    3. Constructions of the Method of Difference Potentials for the Computation of Stressed States of Elastic Compressible Materials

      • Viktor S. Ryaben’kii
      Pages 341-344

    4. Problems of Internal Flows of Viscous Incompressible Fluids

      • Viktor S. Ryaben’kii
      Pages 345-370

    5. An Example of the MDP Algorithm for Computing the Stationary Acoustic Wave Field outside a Solid of Revolution

      • Viktor S. Ryaben’kii
      Pages 371-390
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Keywords

About this book

The method of difference potentials (MDP) was proposed in [1]-[8] and sig­ nificantly developed in [9]-[101] and some other works. The present book describes the current state of the art in the method of difference potentials and is a revised and essentially supplemented version of the author's first book devoted to this method, which was published by "Nauka" in 1987 [100]. This monograph deals with the MDP apparatus and several of its appli­ cations, particularly to the following problems: 1. the numerical solution ofinterior and exterior boundary-value problems for systems of partial differential equations; 2. the construction of conditions at the artificial boundary ofthe compu­ tational domain, which equivalently replace the equations and conditions at infinity in stationary problems of gas flowpast immersed bodies as well as in some other steady-state problems; 3. the spectral approach to the construction of artificial boundary con­ ditions replacing the equations of propagation of physical fields outside the computational domain containing perturbation sources; 4. the construction of artificial boundary conditions on the boundary of the computational domain for numerically solving the scattering problems in large time in a neighborhood of a fixed or a moving scatterer; 5. the statement and solution of stationary mathematical problems of the active shielding of a given subdomain from the influence of perturbation sources located outside the screened subdomain.

Authors and Affiliations

  • Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    Viktor S. Ryaben’kii

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