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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...

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主要な著者: Bichi, Sirajo Lawan, Eshkuvatov, Zainidin K., Nik Long, Nik Mohd Asri, Ismail, Fudziah
フォーマット: Conference or Workshop Item
言語:English
出版事項: IEEE 2015
オンライン･アクセス:http://psasir.upm.edu.my/id/eprint/51899/1/Construction%20of%20cubature%20formula%20for%20double%20integration%20with%20algebraic%20singularity%20by%20spline%20polynomial.pdf
http://psasir.upm.edu.my/id/eprint/51899/
http://ieeexplore.ieee.org/document/7357052/
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spelling my.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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
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.
format Conference or Workshop Item
author Bichi, Sirajo Lawan
Eshkuvatov, Zainidin K.
Nik Long, Nik Mohd Asri
Ismail, Fudziah
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
author_facet Bichi, Sirajo Lawan
Eshkuvatov, Zainidin K.
Nik Long, Nik Mohd Asri
Ismail, Fudziah
author_sort Bichi, Sirajo Lawan
title 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_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_sort construction of cubature formula for double integration with algebraic singularity by spline polynomial
publisher IEEE
publishDate 2015
url http://psasir.upm.edu.my/id/eprint/51899/1/Construction%20of%20cubature%20formula%20for%20double%20integration%20with%20algebraic%20singularity%20by%20spline%20polynomial.pdf
http://psasir.upm.edu.my/id/eprint/51899/
http://ieeexplore.ieee.org/document/7357052/
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score 13.251813

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