Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges.

Citation

Eshkuratov, Zainidin K. and Nik Long, Nik Mohd Asri and Mahiub, Mohammad Abdulkawi (2009) Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges. Journal of Computational and Applied Mathematics, 233 (2). pp. 334-345. ISSN 0377-0427

Abstract

New quadrature formulas (QFs) for evaluating the singular integral (SI) of Cauchy type with unbounded weight function on the edges is constructed. The construction of the QFs is based on the modification of discrete vortices method (MMDV) and linear spline interpolation over the finite interval [−1,1]. It is proved that the constructed QFs converge for any singular point x not coinciding with the end points of the interval [−1,1]. Numerical results are given to validate the accuracy of the QFs. The error bounds are found to be of order O(hα|lnh|) and O(h|lnh|) in the classes of functions Hα([−1,1]) and C1([−1,1]), respectively.

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Additional Metadata

Item Type:	Article
Subject:	Singular integrals
Subject:	Numerical integration
Divisions:	Faculty of Science
DOI Number:	https://doi.org/10.1016/j.cam.2009.07.034
Publisher:	Elsevier
Keywords:	Singular integral; Quadrature formula; Discrete vortices method; Spline approximation; Modification
Depositing User:	Najwani Amir Sariffudin
Date Deposited:	25 Apr 2013 03:18
Last Modified:	14 Sep 2015 07:25
Altmetrics:	http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1016/j.cam.2009.07.034
URI:	http://psasir.upm.edu.my/id/eprint/16403
Statistic Details:	View Download Statistic

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