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

A. I. Fedotov

Archivum Mathematicum (2002)

  • Volume: 038, Issue: 1, page 1-13
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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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 038.1 (2002): 1-13. <http://eudml.org/doc/248939>.

@article{Fedotov2002,
abstract = {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.},
author = {Fedotov, A. I.},
journal = {Archivum Mathematicum},
keywords = {singular integral equations; periodic pseudodifferential equations; Galerkin method; collocation method; singular integral equations; periodic pseudodifferential equations; Galerkin method; collocation method},
language = {eng},
number = {1},
pages = {1-13},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations},
url = {http://eudml.org/doc/248939},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Fedotov, A. I.
TI - On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 1
SP - 1
EP - 13
AB - 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.
LA - eng
KW - singular integral equations; periodic pseudodifferential equations; Galerkin method; collocation method; singular integral equations; periodic pseudodifferential equations; Galerkin method; collocation method
UR - http://eudml.org/doc/248939
ER -

References

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