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Method of Difference Potentials and Its Applications : Springer Series in Computational Mathematics - V.S. Ryabenkii

Method of Difference Potentials and Its Applications

Springer Series in Computational Mathematics

By: V.S. Ryabenkii, N.K. Kulman (Translator)

Hardcover Published: 6th November 2001
ISBN: 9783540426332
Number Of Pages: 538

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The first English edition of a well-known Russian monograph. This book presents the method of difference potentials first proposed by the author in 1969, and contains illustrative examples and new algorithms for solving applied problems of gas dynamics, diffraction, scattering theory, and active noise screening.

Preface to the English Edition
From the Preface to the Russian Edition
Introductionp. 1
Justification of Algorithms of the Method of Difference Potentials for Calculating Numerical Solutions of Interior Boundary-Value Problems for the Laplace Equation
Preliminariesp. 37
Differential and Difference Potentialsp. 53
Reduction of Boundary-Value Problems for the Laplace Equation to Boundary Equations of Calderon-Seeley Typep. 81
Numerical Solution of Boundary-Value Problemsp. 87
General Constructions of Surface Potentials and Boundary Equations on the Basis of the Concept of a Clear Trace
Generalized Potentials and Boundary Equations with Projections for Differential Operatorsp. 141
General Constructions of Potentials and Boundary Equations for Difference Operatorsp. 159
Lazarev's Results on the Algebraic Structure of the Set of Surface Potentials of a Linear Operatorp. 207
A General Scheme of the Method of Difference Potentials for the Numerical Solution of Differential and Difference Boundary-Value Problems of Mathematical Physics
A General Scheme of the Method of Difference Potentials for Differential Problemsp. 217
Illustrations of Constructions of the Method of Difference Potentialsp. 273
General Scheme of the Method of Difference Potentials for Solving Numerically the Difference Analogs of Differential Boundary-Value Problemsp. 291
Examples of MDP Algorithms for Solving Numerically Boundary-Value Problems of Mathematical Physics
The Tricomi Problemp. 329
Constructions of the Method of Difference Potentials for the Computation of Stressed States of Elastic Compressible Materialsp. 341
Problems of Internal Flows of Viscous Incompressible Fluidsp. 345
An Example of the MDP Algorithm for Computing the Stationary Acoustic Wave Field outside a Solid of Revolutionp. 371
Artificial Boundary Conditions for Stationary Problems
An Efficient Algorithm for Constructing Artificial Boundary Conditions for a Model Problemp. 395
On the Results of the Application of the Method of Difference Potentials to the Construction of Artificial Boundary Conditions for External Flow Computationsp. 403
General Constructions of Difference Nonreflecting Artificial Boundary Conditions for Time-Dependent Problems
Nonreflecting Difference Conditions on the Moving and Shape Varying Boundary of the Computational Domainp. 445
Spectral Approach to the Construction of Nonreflecting Boundary Conditionsp. 461
Nonreflecting Artificial Boundary Conditions for Replacing the Rejected Equations with Lacunas
Problem of Constructing NRABCs and the Corresponding Auxiliary Cauchy Problemp. 489
Algorithm for Solving the Cauchy Problem with the Help of Lacunasp. 495
Problems of Active Shielding and Imitation
Active Shielding Controlp. 515
Difference Imitation Problemsp. 519
Appendixp. 523
Referencesp. 525
Indexp. 537
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540426332
ISBN-10: 3540426337
Series: Springer Series in Computational Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 538
Published: 6th November 2001
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 3.81
Weight (kg): 2.13