On a numerical method of the solution of singular integral equations

Many boundary value problems for elliptical equations in Me domains with corner points can be reduced to Me singular integral equations (SIE) with moving and fixed singularities of Cauchy type. Collocation procedure over the special nodes with the following Gauss-Jacobi quadrature application is commonly used for these equations solution. But on Me one hand using of Jacobi polynomials zeros as Me collocation points [1] leads to some error in Gauss-Jacobi quadrature for singular integral on the other hand evaluation of second kind of Jacobi function zeros [2] calls essential numerical difficulties. Our aim is to ebeborate economical algorithm of SIE with fixed singularities numerical solution. For Mis aim attaining we coutract quadrature formulas for Cauchy type singular integrals numerical evaluation.