Direct methods for numerical solution of singular integro-differential equations in classical Hölder spaces (case γ ≠ 0)

Abstract

In this article we elaborate the numerical schemes of the collocation and quadrature- interpolation methods for the approximate solution of the singular integro-differential equations when the kernel has a weak singularity. The equations are defined on the arbitrary smooth closed contour of complex plane. The collocation and quadrature-interpolation methods are based on the descritization using Fejer points. Theoretical background for these methods is to be laid in classical Holder spaces.