Convergence of the collocation method and the mechanical quadrature method for systems of singular integro-differential equations in Lebesgue spaces

Computational schemes for the collocation method and the mechanical quadrature method for the approximate solution of systems of singular integro-differential equations with a Cauchy kernel are elaborated. The case where the systems of equations are defined on an arbitrary smooth closed contour of a...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2012-09, Vol.236 (15), p.3796-3804
Main Authors: Caraus, Iurie, Al Faqih, Feras M.
Format: Article
Language:English
Subjects:
Approximation
Collocation method
Collocation methods
Computation
Convergence
Fejér points
Lebesgue spaces
Mathematical analysis
Mathematical models
Quadratures
Shape
Systems of singular integro-differential equations
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Summary:Computational schemes for the collocation method and the mechanical quadrature method for the approximate solution of systems of singular integro-differential equations with a Cauchy kernel are elaborated. The case where the systems of equations are defined on an arbitrary smooth closed contour of a complex plane is examined. The methods researched are based on Fejér points. Estimates of the rate of convergence in Lebesgue space are obtained.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2012.01.026