Singular Integral Equations and Discrete Vortices
VSP International Science Publishers (Verlag)
978-90-6764-207-1 (ISBN)
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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.
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
| Erscheint lt. Verlag | 1.8.1996 |
|---|---|
| Verlagsort | Zeist |
| Sprache | englisch |
| Gewicht | 880 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| ISBN-10 | 90-6764-207-X / 906764207X |
| ISBN-13 | 978-90-6764-207-1 / 9789067642071 |
| Zustand | Neuware |
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