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

Abstract

The present paper deals with the justification of solvability conditions and properties of solutions for weakly singular integro-differential equations by collocation and mechanical quadrature methods. The equations are defined on an arbitrary smooth closed contour of the complex plane. Error estimates and convergence for the investigated methods are established in Lebesgue spaces.