Some remarks on the numerical solution of cauchy-type singular integral equations with index equal to —1

Several remarks concerning the Gauss-, Radau- and Lobatto-Jacobi direct quadrature methods of numerical solution of Cauchy-type singular integral equations of the first or the second kind with index equal to −1 are made. These remarks concern mainly the construction of the system of linear algebraic equations to which the above equations are reduced by using an appropriate number of collocation points. The same remarks apply also to the special cases where the Gauss-, Radau- and Lobatto-Chebyshev quadrature methods are used. These remarks are of particular interest for the numerical solution of smooth contact problems in the theory of elasticity.