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

Authors:
Iurie Caraus;Feras M. Al Faqih
Affiliations:
Moldova State University, Mateevici 60 str., Chisinau, Moldova, MD-2009, Republic of Moldova;King Faisal University, Department of Mathematics and Statistics, Al Hafouf 1982, P.O. Box 5909, Saudi Arabia
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

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 Fejer points. Estimates of the rate of convergence in Lebesgue space are obtained.