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*A. I. Fedotov*

On convergence of the polynomial collocation method

for singular integral equations and periodic pseudodifferential equations

*(Lobachevskii Journal of Mathematics,
Vol.7, pp.3-14 )*

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.

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