An accurate spline polynomial cubature formula for double integration with logarithmic singularity
The paper studied the integration of logarithmic singularity problem J(ӯ) = ∫∫Δζ(ӯ)log|ӯ - ӯ 0∗|dA, where ӯ=(α,β), y0=(α0,β0) the domain Δ is rectangle Δ = [r1, r2] × [r3, r4], the arbitrary point ӯ ϵ Δ and the fixed point ӯ0 ϵ Δ. The given density function ζ(ӯ), is smooth on the rectangular domain...
| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57194/1/An%20accurate%20spline%20polynomial%20cubature%20formula%20for%20double%20integration%20with%20logarithmic%20singularity.pdf |
| _version_ | 1825931564249251840 |
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| author | Bichi, Sirajo Lawan Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri Bello, M. Y. |
| author_facet | Bichi, Sirajo Lawan Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri Bello, M. Y. |
| author_sort | Bichi, Sirajo Lawan |
| collection | UPM |
| description | The paper studied the integration of logarithmic singularity problem J(ӯ) = ∫∫Δζ(ӯ)log|ӯ - ӯ 0∗|dA, where ӯ=(α,β), y0=(α0,β0) the domain Δ is rectangle Δ = [r1, r2] × [r3, r4], the arbitrary point ӯ ϵ Δ and the fixed point ӯ0 ϵ Δ. The given density function ζ(ӯ), is smooth on the rectangular domain Δ and is in the functions class C2,τ (Δ). Cubature formula (CF) for double integration with logarithmic singularities (LS) on a rectangle Δ is constructed by applying type (0, 2) modified spline function DΓ(P). The results obtained by testing the density functions ζ(ӯ) as linear and absolute value functions shows that the constructed CF is highly accurate. |
| first_indexed | 2024-03-06T09:28:39Z |
| format | Conference or Workshop Item |
| id | upm.eprints-57194 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:28:39Z |
| publishDate | 2016 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | upm.eprints-571942017-09-08T09:42:02Z http://psasir.upm.edu.my/id/eprint/57194/ An accurate spline polynomial cubature formula for double integration with logarithmic singularity Bichi, Sirajo Lawan Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri Bello, M. Y. The paper studied the integration of logarithmic singularity problem J(ӯ) = ∫∫Δζ(ӯ)log|ӯ - ӯ 0∗|dA, where ӯ=(α,β), y0=(α0,β0) the domain Δ is rectangle Δ = [r1, r2] × [r3, r4], the arbitrary point ӯ ϵ Δ and the fixed point ӯ0 ϵ Δ. The given density function ζ(ӯ), is smooth on the rectangular domain Δ and is in the functions class C2,τ (Δ). Cubature formula (CF) for double integration with logarithmic singularities (LS) on a rectangle Δ is constructed by applying type (0, 2) modified spline function DΓ(P). The results obtained by testing the density functions ζ(ӯ) as linear and absolute value functions shows that the constructed CF is highly accurate. AIP Publishing 2016 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57194/1/An%20accurate%20spline%20polynomial%20cubature%20formula%20for%20double%20integration%20with%20logarithmic%20singularity.pdf Bichi, Sirajo Lawan and Eshkuvatov, Zainidin K. and Nik Long, Nik Mohd Asri and Bello, M. Y. (2016) An accurate spline polynomial cubature formula for double integration with logarithmic singularity. In: 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016), 26-28 Jan. 2016, Kuala Lumpur, Malaysia. (pp. 1-8). 10.1063/1.4952513 |
| spellingShingle | Bichi, Sirajo Lawan Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri Bello, M. Y. An accurate spline polynomial cubature formula for double integration with logarithmic singularity |
| title | An accurate spline polynomial cubature formula for double integration with logarithmic singularity |
| title_full | An accurate spline polynomial cubature formula for double integration with logarithmic singularity |
| title_fullStr | An accurate spline polynomial cubature formula for double integration with logarithmic singularity |
| title_full_unstemmed | An accurate spline polynomial cubature formula for double integration with logarithmic singularity |
| title_short | An accurate spline polynomial cubature formula for double integration with logarithmic singularity |
| title_sort | accurate spline polynomial cubature formula for double integration with logarithmic singularity |
| url | http://psasir.upm.edu.my/id/eprint/57194/1/An%20accurate%20spline%20polynomial%20cubature%20formula%20for%20double%20integration%20with%20logarithmic%20singularity.pdf |
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