Collocation and Quadrature Methods for Solving Singular Integral Equations with Piecewise Continuous Coefficients

The computation schemes of collocation and mechanical quadrature methods for approximate solving of the complete singular integral equations with piecewise continuous coefficients and a regular kernel with weak singularity are elaborated. The case when the equations are defined on the unit circumference of the complex plane is examined. The sufficient conditions for the convergence of these methods in the space $L_2$ are obtained.