Singular Integral Equations and Discrete Vortices / I. K. Lifanov.

Format:

Book

Author/Creator:

Lifanov, I. K., author.

Language:

English

Subjects (All):

Integral equations.

Singular integrals.

Physical Description:

1 online resource (488 pages)

Edition:

Reprint 2018

Place of Publication:

Berlin ; Boston : De Gruyter, [2018]

Language Note:

In English.

Summary:

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.

Contents:

Frontmatter

CONTENTS

Introduction

PART I . ELEMENTS OF THE THEORY OF SINGULAR INTEGRAL EQUATIONS

Chapter 1. One-dimensional singular integrals

Chapter 2. One-dimensional singular integral equations

Chapter 3. 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

Chapter 4. Boundary problems for Laplace and Helmholtz equations. Plane case

Chapter 5. Boundary problems for the Laplace and the Helmholtz equations. Spatial case

Chapter 6. Stationary problems of aerohydrodynamics. Plane case

Chapter 7. Stationary aerohydrodynamic problems. Spatial case

Chapter 8. Nonstationary aerohydrodynamic problems

Chapter 9. Determination of aerohydrodynamic characteristics

Chapter 10. Some electrostatic problems

Chapter 11. Some problems of mathematical physics

Chapter 12. Problems in elasticity theory

PART III. CALCULATION OF SINGULAR INTEGRAL VALUES

Chapter 13. Quadrature formulas of the method of discrete vortices for one-dimensional singular integrals

Chapter 14. Quadrature formulas of interpolation type for one-dimensional singular integrals and operators

Chapter 15. Quadrature formulas for multiple and multidimensional singular integrals

Chapter 16. Proving the Poincare-Bertrand formula with the help of quadrature formulas

PART IV. NUMERICAL SOLUTION OF SINGULAR INTEGRAL EQUATIONS

Chapter 17. Equations of the first kind. The numerical method of discrete vortex type

Chapter 18. Equations of the first kind. Interpolation methods

Chapter 19. Equations of the second kind. Interpolation methods

Chapter 20. Singular integral equations with multiple Cauchy integrals

PART V. DISCRETE MATHEMATICAL MODELS AND CALCULATION EXAMPLES

Chapter 21. Discrete vortex systems

Chapter 22. Discrete vortex method for plane stationary problems

Chapter 23. Method of discrete vortices for spatial stationary problems

Chapter 24. Method of discrete vortices in nonstationary problems of aerodynamics

Chapter 25. Numerical method of discrete singularities in electrodynamic problems and elasticity theory

References

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9783110926040

3110926040

OCLC:

1076440517