Singular integral equations of the second kind with generalized Cauchy-type kernels and variable coefficients

A numerical solution method is presented for singular integral equations of the second kind with a generalized Cauchy kernel and variable coefficients. The solution is constructed in the form of a product of regular and weight functions. The weight function possesses complex singularities at the ends of the interval. The parameters defining the power of these singularities are obtained by solving for the characteristic equations. A Gauss-Chebychev quadrature formula is utilized in the numerical solution of the integral equations. Benchmark examples are considered in order to illustrate the validity of the solution method.