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Singular integral equations and discrete vortices. (English) Zbl 0871.65110

Utrecht: VSP. ix, 475 p. (1996).
In the first part of this book the elements of the theory of singular integrals and singular integral equations in the class of absolutely integrable and non-integrable functions are considered. Moreover, the same equations with multiple integrals of Cauchy and Hilbert type are presented. In the second part, the elements of potential theory for the Helmholtz equations are given. Also, the pair sum equations and some plane problems from the theory of elasticity are considered.
The third part contains the methods of calculations for different one-dimensional and two-dimensional singular integrals. The above quadrature formulas are applied in the fourth part of this book to the numerical solution of singular integral equations of the 1st and 2nd kind with constant and variable coefficients.
The last part is devoted to discrete mathematical models of some problems in aerodynamics, electrodynamics and the theory of elasticity.
For the review of the Russian original [Moskva: TOO Yanus. 520 p. (1995)] see Zbl 0904.73001.
Reviewer: L.Hącia (Poznań)

MSC:

65R20 Numerical methods for integral equations
31A10 Integral representations, integral operators, integral equations methods in two dimensions
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
45Exx Singular integral equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
74B05 Classical linear elasticity
65D32 Numerical quadrature and cubature formulas

Citations:

Zbl 0904.73001
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