On the stability of the classical collocation method for Cauchy-type singular integral equations

AbstractThe classical collocation method for Cauchy-type singular integral equations of the second kind on an interval using Gaussian quadrature rules with respect to Jacobi nodes is investigated. In general, the nodes and the weights of the quadrature rules can only be evaluated approximately. In the present paper the question is answered how precise our knowledge about them must be in order to ensure that the corresponding algebraic system of equations is solvable yet and its solution is close to the solution of the exact system