# On convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations

## (*Lobachevskii Journal of Mathematics, Volume VII*)

We prove the convergence of polynomial collocation method for periodic singular integral, pseudodifferential and the systems of pseudodifferential equations in Sobolev spaces *H*^{s} via the equivalence between the collocation and modified Galerkin methods. The boundness of the Lagrange interpolation operator in this spaces when *s>1/2* allows to obtain the optimal error estimate for the approximate solution i.e. it has the same rate as the best approximation of the exact solution by the polynomials.