Overview
- 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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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.
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Table of contents (23 chapters)
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Front Matter
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Introduction
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Justification of Algorithms of the Method of Difference Potentials for Calculating Numerical Solutions of Interior Boundary-Value Problems for the Laplace Equation
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Front Matter
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General Constructions of Surface Potentials and Boundary Equations on the Basis of the Concept of a Clear Trace
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Front Matter
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A General Scheme of the Method of Difference Potentials for the Numerical Solution of Differential and Difference Boundary-Value Problems of Mathematical Physics
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Front Matter
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Examples of MDP Algorithms for Solving Numerically Boundary-Value Problems of Mathematical Physics
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Front Matter
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Authors and Affiliations
Bibliographic Information
Book Title: Method of Difference Potentials and Its Applications
Authors: Viktor S. Ryaben’kii
Series Title: Springer Series in Computational Mathematics
DOI: https://doi.org/10.1007/978-3-642-56344-7
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2002
Hardcover ISBN: 978-3-540-42633-2Published: 06 November 2001
Softcover ISBN: 978-3-642-62715-6Published: 09 October 2012
eBook ISBN: 978-3-642-56344-7Published: 06 December 2012
Series ISSN: 0179-3632
Series E-ISSN: 2198-3712
Edition Number: 1
Number of Pages: XVIII, 538
Additional Information: Original Russian edition published by Fizmatlit, Moscow, 2001
Topics: Analysis, Numerical Analysis, Functions of a Complex Variable, Theoretical, Mathematical and Computational Physics