On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations
Fedotov, A. I.
Archivum Mathematicum, Tome 038 (2002), p. 1-13 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2002-01-01
Classification:  45E05,  47G30,  65N35,  65R20 
@article{107814,
     author = {A. I. Fedotov},
     title = {On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations},
     journal = {Archivum Mathematicum},
     volume = {038},
     year = {2002},
     pages = {1-13},
     zbl = {1087.65109},
     mrnumber = {1899563},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107814}
}

Fedotov, A. I. On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations. Archivum Mathematicum, Tome 038 (2002) pp. 1-13. http://gdmltest.u-ga.fr/item/107814/

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