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An accurate spline polynomial cubature formula for double integration with logarithmic singularity


Citation

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).

Abstract / Synopsis

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.


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Additional Metadata

Item Type: Conference or Workshop Item (Paper)
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1063/1.4952513
Publisher: AIP Publishing
Keywords: Logarithmic singularity; Cubature formula
Depositing User: Nabilah Mustapa
Date Deposited: 08 Sep 2017 17:42
Last Modified: 08 Sep 2017 17:42
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1063/1.4952513
URI: http://psasir.upm.edu.my/id/eprint/57194
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