Approximate solution of singular integro- differential equations in generalized Hölder spaces

We have elaborated the numerical schemes of collocation methods and mechanical quadrature methods for approximate solution of singular integro- differential equations with kernels of Cauchy type. The equations are defined on the arbitrary smooth closed contours of complex plane. The researched methods are based on Fejér points. Theoretical background of collocation methods and mechanical quadrature methods has been obtained in Generalized Hölder spaces.