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

Abstract

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.

Numerical Solution of Weakly Singular Integrodifferential Equations on Closed Smooth Contour in Lebesgue Spaces

“…We note that the convergence of the collocation method, reduction method and mechanical quadrature method for SIDE and systems of such equations in generalized Hölder spaces has been obtained in [16][17][18] . The equations are given on an arbitrary smooth closed contour not weakly SIDE .…”

A Novel Third Order Numerical Method for Solving Volterra Integro-Differential Equations

“…Dehghan and Salehi [11] developed a numerical scheme based on the moving least square method for these equations. Singular IDEs in generalized Holder spaces are solved by using collocation and mechanical quadrature methods in [12]. Saeedi et al [13] described the operational Tau method for solving nonlinear VIDEs of the second kind.…”