Overview

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. This monograph is divided into five parts and opens with elements of the theory of singular integral equation solutions in the class of absolutely integrable and non-integrable functions. The second part deals with elements of potential theory for the Helmholtz equation, especially with the reduction of Dirichlet and Neumann problems for Laplace and Helmholtz equations to singular integral equations. Part three contains methods of calculation for different one-dimensional and two-dimensional singular integrals. In this part, quadrature formulas of discrete vortex pair type in the plane case and closed vortex frame type in the spatial case for singular integrals are described for the first time. These quadrature formulas are applied to numerical solutions of singular integral equations of the 1st and 2nd kind with constant and variable coefficients, in part four of the book. Finally, discrete mathematical models of some problems in aerodynamics, electrodynamics and elasticity theory are given.

Full Product Details

Author:   I. K. Lifanov
Publisher:   Brill
Imprint:   VSP International Science Publishers
Weight:   0.900kg
ISBN:  

9789067642071

ISBN 10:   906764207
Pages:   476
Publication Date:   August 1996
Recommended Age:   College Graduate Student
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Introduction PART I. ELEMENTS OF THE THEORY OF SINGULAR INTEGRAL EQUATIONS One-dimensional singular integrals One-dimensional singular integral equations Singular integral equations with multiple Cauchy-type integrals PART II. REDUCING OF BOUNDARY PROBLEMS OF MATHEMATICAL PHYSICS AND SOME APPLIED FIELDS TO THE SINGULAR INTEGRAL EQUATIONS Boundary problems for Laplace and Helmholtz equations. Plane case Boundary problems for the Laplace and the Helmholtz equations. Spatial case Stationary problems of aerohydrodynamics. Plan case Stationary aerohydrodynamic problems. Spatial case Nonstationary aerohydrodynamic problems Determination of aerohydrodynamic characteristics Some electrostatic problems Some problems of mathematical physics Problems in elasticity theory PART III. CALCULATION OF SINGULAR INTEGRAL VALUES Quadrature formulas of the method of discrete vortices for one-dimensional singular integrals Quadrature formulas of interpolation type for one-dimensional singular integrals and operators Singular integral with Hilbert kernel Singular integral on a circle Singular integral on a segment Quadrature formulas for multiple and multidimensional singular integrals Proving the Poincare-Bertrand formula with the help of quadrature formulas PART IV. NUMERICAL SOLUTION OF SINGULAR INTEGRAL EQUATIONS Equations of the first kind. The numerical method of discrete vortex type Equations of the first kind. Interpolation methods Equations of the second kind. Interpolation methods Singular integral equations with multiple Cauchy integrals PART V. DISCRETE MATHEMATICAL MODELS AND CALCULATION EXAMPLES Discrete vortex systems Discrete vortex method for plane stationary problems Method of discrete vortices for spatial stationary problems Method of discrete vortices in nonstationary problems of aerodynamics Numerical method of discrete singularities in electrodynamic problems and elasticity theory Main plane electrostatic problem Problems of plane elasticity theory and punch theory References

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