Geodesic
On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations
Archivum mathematicum, Tome 38 (2002) no. 1, pp. 1-13.

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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.
Classification : 45E05, 47G30, 65N35, 65R20
Keywords: singular integral equations; periodic pseudodifferential equations; Galerkin method; collocation method 
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     author = {Fedotov, A. I.},
     title = {On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations},
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Fedotov, A. I. On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations. Archivum mathematicum, Tome 38 (2002) no. 1, pp. 1-13. http://geodesic.mathdoc.fr/item/ARM_2002__38_1_a0/