Construction of cubature formula for double integration with algebraic singularity by spline polynomial
In this note, singular integration problems of the form Hα (h) = ∫Ω∫ h(x,y)/|-x0|2-α dA, 0 ≤ α ≤ 1, where Ω = [x0,y0] × [b1, b2], x= (x,y) ϵ Ω and fixed point x 0 = (x0,y0) ϵ Ω is considered. The density function h(x, y) is assumed given, continuous and smooth on the rectangle Ω and belong to the cl...
| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
IEEE
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/51899/1/Construction%20of%20cubature%20formula%20for%20double%20integration%20with%20algebraic%20singularity%20by%20spline%20polynomial.pdf |
| _version_ | 1825930619490664448 |
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| author | Bichi, Sirajo Lawan Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri Ismail, Fudziah |
| author_facet | Bichi, Sirajo Lawan Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri Ismail, Fudziah |
| author_sort | Bichi, Sirajo Lawan |
| collection | UPM |
| description | In this note, singular integration problems of the form Hα (h) = ∫Ω∫ h(x,y)/|-x0|2-α dA, 0 ≤ α ≤ 1, where Ω = [x0,y0] × [b1, b2], x= (x,y) ϵ Ω and fixed point x 0 = (x0,y0) ϵ Ω is considered. The density function h(x, y) is assumed given, continuous and smooth on the rectangle Ω and belong to the class of functions C2,α(Ω). Cubature formula for double integrals with algebraic singularity on a rectangle is constructed using the modified spline function SΩ(P) of type (0, 2). Highly accurate numerical results for the proposed method is given for both tested density function h(x, y) as linear, quadratic and absolute value functions. The results are in line with the theoretical findings. |
| first_indexed | 2024-03-06T09:14:19Z |
| format | Conference or Workshop Item |
| id | upm.eprints-51899 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:14:19Z |
| publishDate | 2015 |
| publisher | IEEE |
| record_format | dspace |
| spelling | upm.eprints-518992017-05-03T04:13:26Z http://psasir.upm.edu.my/id/eprint/51899/ Construction of cubature formula for double integration with algebraic singularity by spline polynomial Bichi, Sirajo Lawan Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri Ismail, Fudziah In this note, singular integration problems of the form Hα (h) = ∫Ω∫ h(x,y)/|-x0|2-α dA, 0 ≤ α ≤ 1, where Ω = [x0,y0] × [b1, b2], x= (x,y) ϵ Ω and fixed point x 0 = (x0,y0) ϵ Ω is considered. The density function h(x, y) is assumed given, continuous and smooth on the rectangle Ω and belong to the class of functions C2,α(Ω). Cubature formula for double integrals with algebraic singularity on a rectangle is constructed using the modified spline function SΩ(P) of type (0, 2). Highly accurate numerical results for the proposed method is given for both tested density function h(x, y) as linear, quadratic and absolute value functions. The results are in line with the theoretical findings. IEEE 2015 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/51899/1/Construction%20of%20cubature%20formula%20for%20double%20integration%20with%20algebraic%20singularity%20by%20spline%20polynomial.pdf Bichi, Sirajo Lawan and Eshkuvatov, Zainidin K. and Nik Long, Nik Mohd Asri and Ismail, Fudziah (2015) Construction of cubature formula for double integration with algebraic singularity by spline polynomial. In: 7th International Conference on Research and Education in Mathematics (ICREM7), 25-27 Aug. 2015, Renaissance Kuala Lumpur Hotel, Malaysia. (pp. 193-198). http://ieeexplore.ieee.org/document/7357052/ 10.1109/ICREM.2015.7357052 |
| spellingShingle | Bichi, Sirajo Lawan Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri Ismail, Fudziah Construction of cubature formula for double integration with algebraic singularity by spline polynomial |
| title | Construction of cubature formula for double integration with algebraic singularity by spline polynomial |
| title_full | Construction of cubature formula for double integration with algebraic singularity by spline polynomial |
| title_fullStr | Construction of cubature formula for double integration with algebraic singularity by spline polynomial |
| title_full_unstemmed | Construction of cubature formula for double integration with algebraic singularity by spline polynomial |
| title_short | Construction of cubature formula for double integration with algebraic singularity by spline polynomial |
| title_sort | construction of cubature formula for double integration with algebraic singularity by spline polynomial |
| url | http://psasir.upm.edu.my/id/eprint/51899/1/Construction%20of%20cubature%20formula%20for%20double%20integration%20with%20algebraic%20singularity%20by%20spline%20polynomial.pdf |
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