On the stability of some operator sequences and the approximate solution of singular integral equations with conjugation (Q1804049)

The authors study the spline Galerkin and spline collocation method for singular integral equations of the form \[ \begin{multlined} a(t)x(t)+ {b(t)\over\pi i}\int_ \Gamma {x(\tau)\over \tau-t} d\tau+ c(t)\overline{x(t)}+ {d(t)\over \pi i}\int_ \Gamma {\overline{x(\tau)}\over \tau-t} d\tau+\\ +\int_ \Gamma h_ 1(t,\tau)x(\tau)d\tau+ \int_ \Gamma h_ 2(t,\tau)\overline{x(\tau)}d\tau= f(t),\quad t\in\Gamma,\end{multlined} \] where \(\Gamma\) is a simple, smooth and closed curve on the plane.