The approximate solution of singular integral equations

A computational scheme of collocation type is proposed for a singular linear integral equation with a power singularity in the regular integral and the justification is given. The results obtained are used to justify the approximate solution of the singular integral equation $$Kx equiv a(t)x(t) + frac{{b(t)}}{{pi i}}smallint _{left| tau right| = 1} frac{{x(tau )dtau }}{{tau - t}} + frac{1}{{2pi i}}smallint _{left| tau right| = 1} frac{{h|t,tau )x(tau )}}{{left| {tau - t} right|^delta }}dtau = f(t)$$ by a modification of the method of minimal residuals.