Finite-dimensional approximations of singular integrals and direct methods of solution of singular integral and integrodifferential equations

Flow around permeable and thick airfoils and numerical solution of singular integral equations

“…It is to be noted that there are plenty of works (see, e.g. [5,10,11,16,17]) that deal with numerical solution of singular integral equations on the segment [-1,1].…”

New Recursive Representations for the Favard Constants with Application to Multiple Singular Integrals and Summation of Series

“…It can be noted that Favard constants are connected to approximations that are best in a pointwise sense in comparison, for instance, with the Lebesgue constants which are connected to approximations that are best in a least-squares sense (Fourier series) [5]. The Favard constants play also an important role in estimating optimal quadrature and cubature formulas, calculation of singular integrals, some classes of differential, integrodifferential and integral equations [18][19][20][21][22][23][24], and in other areas.…”

Cauchy-type singular integral equation with constant coefficients on the real line

“…The numerical solution of Cauchy-type singular integral equations on the finite interval were investigated by many authors [1][2][3]6,12]. In addition, some papers discussed the approximate solution of Cauchy-type singular integral equation on the real half-line [9,11].…”