Method of difference potentials and its applications /
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| Author / Creator: | Ri͡abenʹkiĭ, V. S. (Viktor Solomonovich). |
|---|---|
| Uniform title: | Metod raznostnykh potent͡sialov dli͡a nekotorykh zadach mekhaniki sploshnykh sred. English |
| Imprint: | Berlin ; New York : Springer, c2002. |
| Description: | xviii, 538 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Springer series in computational mathematics, 0179-3632 ; 30 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4661788 |
Table of Contents:
- Pt. I. Justification of Algorithms of the Method of Difference Potentials for Calculating Numerical Solutions of Interior Boundary-Value Problems for the Laplace Equation
- 1. Preliminaries
- 2. Differential and Difference Potentials
- 3. Reduction of Boundary-Value Problems for the Laplace Equation to Boundary Equations of Calderon-Seeley Type
- 4. Numerical Solution of Boundary-Value Problems
- Pt. II. General Constructions of Surface Potentials and Boundary Equations on the Basis of the Concept of a Clear Trace
- 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
- Pt. III. A General Scheme of the Method of Difference Potentials for the Numerical Solution of Differential and Difference Boundary-Value Problems of Mathematical Physics
- 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 Scheme of the Method of Difference Potentials for Solving Numerically the Difference Analogs of Differential Boundary-Value Problems
- Pt. IV. Examples of MDP Algorithms for Solving Numerically Boundary-Value Problems of Mathematical Physics
- 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
- Pt. V. Artificial Boundary Conditions for Stationary Problems
- 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
- Pt. VI. General Constructions of Difference Nonreflecting Artificial Boundary Conditions for Time-Dependent Problems
- 1. Nonreflecting Difference Conditions on the Moving and Shape Varying Boundary of the Computational Domain
- 2. Spectral Approach to the Construction of Nonreflecting Boundary Conditions
- Pt. VII. Nonreflecting Artificial Boundary Conditions for Replacing the Rejected Equations with Lacunas
- 1. Problem of Constructing NRABCs and the Corresponding Auxiliary Cauchy Problem
- 2. Algorithm for Solving the Cauchy Problem with the Help of Lacunas
- Pt. VIII. Problems of Active Shielding and Imitation
- 1. Active Shielding Control
- 2. Difference Imitation Problems.
