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Singular Integral Equations and Discrete Vortices (Hardcover, Reprint 2018)
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Singular Integral Equations and Discrete Vortices (Hardcover, Reprint 2018)
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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.
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