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＜電子ブック＞
Method of Difference Potentials and Its Applications / by Viktor S. Ryaben'kii
(Springer Series in Computational Mathematics. ISSN:21983712 ; 30)

版	1st ed. 2002.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2002
本文言語	英語
大きさ	XVIII, 538 p : online resource
著者標目	*Ryaben'kii, Viktor S author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Numerical analysis LCSH:Functions of complex variables LCSH:Mathematical physics FREE:Analysis FREE:Numerical Analysis FREE:Functions of a Complex Variable FREE:Theoretical, Mathematical and Computational Physics
一般注記	I. Justification of Algorithms of the Method -- 1. Preliminaries -- 2. Differential and Difference Potentials -- 3. Reduction of Boundary-Value Problems for the Laplace Equation to Boundary Equations of Calderón-Seeley Type -- 4. Numerical Solution of Boundary-Value Problems -- II. General Constructions of Surface Potentials -- 1. Generalized Potentials and Boundary Equations with Projections for Differential Operators -- 2. General Constructions of Potentials and Boundary Equations for Difference Operators -- 3. Lazarev’s Results on the Algebraic Structure of the Set of Surface Potentials of a Linear Operator -- III. A General Scheme of the Method of Difference -- 1. A General Scheme of the Method of Difference Potentials for Differential Problems -- 2. Illustrations of Constructions of the Method of Difference Potentials -- 3. General Scheine of the Method of Difference Potentials for Solving Numerically the Difference Analogs of Differential Boundary-Value Problems -- IV. Examples of MDP Algorithms for Solving -- 1. The Tricomi Problem -- 2. Constructions of the Method of Difference Potentials for the Computation of Stressed States of Elastic Compressible Materials -- 3. Problems of Internal Flows of Viscous Incompressible Fluids -- 4. An Example of the MDP Algorithm for Computing the Stationary Acoustic Wave Field outside a Solid of Revolution -- V. Artificial Boundary Conditions -- 1. An Efficient Algorithm for Constructing Artificial Boundary Conditions for a Model Problem -- 2. On the Results of the Application of the Method of Difference Potentials to the Construction of Artificial Boundary Conditions for External Flow Computations -- VI. General Constructions of Difference -- 1. Nonreflecting Difference Conditions on the Moving and Shape Varying Boundary of the ComputationalDomain -- 2. Spectral Approach to the Construction of Nonreflecting Boundary Conditions -- VII. Nonreflecting Artificial Boundary Conditions -- 1. Problem of Constructing NRABCs and the Corresponding Auxiliary Cauchy Problem -- 2. Algorithm for Solving the Cauchy Problem with the Help of Lacunas -- VIII. Problems of Active Shielding and Imitation -- 1. Active Shielding Control -- 2. Difference Imitation Problems -- References 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 HTTP:URL=https://doi.org/10.1007/978-3-642-56344-7

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