Approximate solution to integral equation with logarithmic kernel of special form (Q283077)

The authors are concerned with the study of harmonic functions \(u=u(r,\varphi)\) in the open unit disc subject to the boundary conditions \[ \Big(\frac{\partial u}{\partial r}+q(\varphi)u\Big)\Big|_{r=1}=f(\varphi),\quad \varphi\in [-\pi,\pi], \] where \(f\) and \(q\) are given functions on the interval \([-\pi,\pi]\). Such a boundary value problem is first transformed into an integral equation. The main results of the paper present uniform estimates of deviations of the quadrature formula and the approximate solution to the integral equation.