Approximate Solution of Singular Integral Equations with Negative Index

Abstract

This paper is devoted to investigating a class of linear singular integral equations with a negative index on a closed, simple and smooth curve. In this paper, we propose the quadrature method for the approximate solution of the linear singular integral equations with negative index. Sufficient conditions are given for the convergence of this method in HÖlder space. Key Words: Linear singular integral equation, Index of singular integral equation, Quadrature method.