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Media type:
E-Book
Title:
Singular Integral Equations and Discrete Vortices
Contains:
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