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

• Main Authors: Bichi, Sirajo Lawan, Eshkuvatov, Zainidin K., Nik Long, Nik Mohd Asri, Bello, M. Y.
• Format: Conference or Workshop Item
• Language: English
• Published: AIP Publishing 2016
• Online Access: http://psasir.upm.edu.my/id/eprint/57194/1/An%20accurate%20spline%20polynomial%20cubature%20formula%20for%20double%20integration%20with%20logarithmic%20singularity.pdf; http://psasir.upm.edu.my/id/eprint/57194/
• Institution: Universiti Putra Malaysia

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...