Numerical solution of a class of integral equations arising in two-dimensional aerodynamics

The Chebyshev points of the first kind

“…[29,27,17]. The Hilbert-type integral is interpreted as Cauchy principal value integral, indicated by − , and K(s,t) is a Fredholm kernel [40, p. 72].…”

“…A widely adopted approach for solving (27) is to use Chebyshev points of the first kind as the quadrature points for the evaluation of both the integrals and Chebyshev points of the second kind as the collocation points. The benefits are twofold.…”

Multigrid methods for boundary integral equations

“…Here S can be an open or closed contour. Among the physical examples, we mention the elastostatic problems in shells, composite materials and layered media containing cracks [4,8] and the generalized airfoil equation [3,10] arising in the determination of the compressible flow about a thin airfoil in a ventilated windtunnel.…”

Further Convergence Results for the Weighted Galerkin Method of Numerical Solution of Cauchy-Type Singular Integral Equations

“…Introduction. The problem of convergence of the weighted Galerkin method for the direct numerical solution of one-dimensional, real Cauchy-type singular integral equations of the second kind with constant coefficients on a finite interval (called in the sequel simply singular integral equations) [3], [5], [6], [8], [9], [11], [14] will be considered again. The results obtained supplement previous relevant convergence results [9], [11], [14] and, particularly, those of Linz [11] for singular integral equations of the first kind only.…”

“…This modification consists in basing the convergence results on analogous results for Fredholm integral equations of the second kind [1], [2] and not proceeding directly with the singular integral equations under consideration as in [11]. Although this approach, already used in [3], [6], [8], [9], [14], may not be the most direct, it surely is the most economical, yielding a proof of convergence with little effort and on the basis of the well-known theory for Fredholm integral equations of the second kind [1], [2], N. I. lOAKIMIDIS it is assumed to be possibly unbounded as x -» ± 1. Then [10] The number…”