Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges.
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,...
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| Format: | Article |
| Language: | English English |
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Elsevier
2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/16403/1/Quadrature%20formula%20for%20approximating%20the%20singular%20integral%20of%20Cauchy%20type%20with%20unbounded%20weight%20function%20on%20the%20edges.pdf |
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| author | Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri Mahiub, Mohammad Abdulkawi |
| author_facet | Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri Mahiub, Mohammad Abdulkawi |
| author_sort | Eshkuratov, Zainidin K. |
| collection | UPM |
| description | 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. |
| first_indexed | 2024-03-06T07:37:19Z |
| format | Article |
| id | upm.eprints-16403 |
| institution | Universiti Putra Malaysia |
| language | English English |
| last_indexed | 2024-03-06T07:37:19Z |
| publishDate | 2009 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | upm.eprints-164032015-09-14T07:25:01Z http://psasir.upm.edu.my/id/eprint/16403/ Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges. Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri Mahiub, Mohammad Abdulkawi 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. Elsevier 2009 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/16403/1/Quadrature%20formula%20for%20approximating%20the%20singular%20integral%20of%20Cauchy%20type%20with%20unbounded%20weight%20function%20on%20the%20edges.pdf 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 Singular integrals Numerical integration 10.1016/j.cam.2009.07.034 English |
| spellingShingle | Singular integrals Numerical integration Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri Mahiub, Mohammad Abdulkawi Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges. |
| title | Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges. |
| title_full | Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges. |
| title_fullStr | Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges. |
| title_full_unstemmed | Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges. |
| title_short | Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges. |
| title_sort | quadrature formula for approximating the singular integral of cauchy type with unbounded weight function on the edges |
| topic | Singular integrals Numerical integration |
| url | http://psasir.upm.edu.my/id/eprint/16403/1/Quadrature%20formula%20for%20approximating%20the%20singular%20integral%20of%20Cauchy%20type%20with%20unbounded%20weight%20function%20on%20the%20edges.pdf |
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