Approximate solution of a class of singular integral equations of the first kind

In the present paper, we develop an optimal algorithm for the approximate solution of one dimensional singular integral equations with the Cauchy kernel. Here we are engaged in finding the analytical form of the coefficients of the optimal quadrature formula. We apply these coefficients to an approximate solution of the Fredholm singular integral equation of the first kind. Thus, we show the possibility of solving singular integral equations with higher accuracy using the optimal quadrature formula based on the Sobolev method.