Approximate Solution of Singular Integro-Differential Equations for displaced Fejer Points

Abstract: The main proposal of this article is the investigation and theoretical background of the direct-approximate methods for the numerical solution of singular integro-differential(SIDE) equations(Cauchy type kernel) with unknown function defined on the smooth contours of the Lypunov type. The equations are studied in the Lebesgue spaces. The SIDE are defined on the displaced Fej´er points of complex plane. The numerical schemes of collocation and mechanical quadrature methods for the SIDE defined on an arbitrary smooth closed contour of complex plane are elaborated. The theorems of convergence of these methods have been proved in Lebesgue spaces.