Singular Integral Equations and Discrete Vortices (PDF)

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