## On the approximate solution of a class of linear singular integral equations.(Russian)Zbl 0571.65111

The following linear singular equation is studied $(1)\quad a(t)x(t)+(b(t)/\pi i)\int_{\gamma}x(\tau)d\tau /(\tau -t)\ln ((t- \tau)/c)=f(t),\quad t\in \gamma,$ where a(t), b(t), f(t) are continuous functions and $$\gamma$$ is the unit circle in the complex plane, $$c>2$$. The numerical computation of the solution x of equation (1) is based on the collocation method using a polynomial expression for x on the basis of Hölder spaces $$H_{\beta}$$ $$(0<\beta \leq 1)$$. An estimation of the error by numerical computation of the integral $$Bx(t)=(1/\pi i)\int_{\gamma}x(\tau)d\tau /(\tau -t)\ln ((\tau -t)/2)$$ is given, too.
Reviewer: J.Kofroň

### MSC:

 65R20 Numerical methods for integral equations 45E05 Integral equations with kernels of Cauchy type

### Keywords:

error estimates; collocation method; Hölder spaces