On convergence of the method of orthogonal polynomials of the approximate solution оf the second order integral equations with $Π$-kernels - Noreddin , M. M.; Tikhonenko , N. Ya. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
The method of orthogonal polynomials for approximate solution of integral equations of the first kind with Π-kernels is substantiated. The solvability of the corresponding algebraic systems is proved, and estimates for the rate of the convergence of approximate solutions to exact ones are established. The applicability of the method of orthogonal polynomials to approximate solution of integral equations of the second kind with Π-kernels is shown, as well as its high effectiveness in solving integral equations of the first kind with Π-kernels. Concrete Π-kernels, most often occurring in applications, are presented.