Система интегральных уравнений первого рода на отрезке [0,2π ] с логарифмическим ядром

Abstract

A system of integral equations of the first kind with logarithmic kernel, which arises in a number of problems of the diffraction of waves, is studied. The sampling of the system is obtained by the method of discrete singularities. Pairs of Hilbert spaces and operators in them, corresponding to the set and discrete problems are introduced. Using them we prove the unique solvability of the discrete problem and provide a rigorous justification for estimating the rate of convergence of the solution of the discrete problem to the exact solution of the integral equations.