Solution of a class of integral equations with fixed singularities in the kernel by the mechanical quadrature method

Computational schemes for the mechanical quadrature method were constructed on the basis of a simplest interval quadrature formula for Fredholm integral equations of the second kind with fixed integrable singularities in the kernel on the internal and external variables. The theoretical and functional justification of these schemes was given. In particular, the convergence of the method in the space of functions square-integrable in the interval of integration with a weight depending on the characteristics of the integral operator's kernel was proved. The results obtained for the one-dimensional case were also extended to the multidimensional case.