Method of Difference Potentials and Its Applications

  • Viktor S. Ryaben’kii

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

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Introduction

    1. 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
    2. Viktor S. Ryaben’kii
      Pages 37-52
    3. Viktor S. Ryaben’kii
      Pages 53-80
    4. 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

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

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

  7. Artificial Boundary Conditions for Stationary Problems

  8. General Constructions of Difference Nonreflecting Artificial Boundary Conditions for Time-Dependent Problems

  9. Nonreflecting Artificial Boundary Conditions for Replacing the Rejected Equations with Lacunas

    1. Front Matter
      Pages 485-487
  10. Problems of Active Shielding and Imitation

    1. Front Matter
      Pages 511-513
    2. Viktor S. Ryaben’kii
      Pages 515-518
    3. Viktor S. Ryaben’kii
      Pages 519-522
  11. Back Matter
    Pages 523-538

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.


Integral equation Potential active shielding artificial boundary conditions for flow boundary-value problems diffraction mathematical physics methods of difference potentials numerical solution of boundary-value problems pseudodifferential boundary equations scattering problems scattering theory

Authors and affiliations

  • Viktor S. Ryaben’kii
    • 1
  1. 1.Keldysh Institute for Applied MathematicsRussian Academy of SciencesMoscowRussia

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-62715-6
  • Online ISBN 978-3-642-56344-7
  • Series Print ISSN 0179-3632
  • Buy this book on publisher's site