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...
| প্রধান লেখক: | , , , |
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| বিন্যাস: | Conference or Workshop Item |
| ভাষা: | English |
| প্রকাশিত: |
AIP Publishing
2016
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| অনলাইন ব্যবহার করুন: | http://psasir.upm.edu.my/id/eprint/57194/1/An%20accurate%20spline%20polynomial%20cubature%20formula%20for%20double%20integration%20with%20logarithmic%20singularity.pdf |
| সংক্ষিপ্ত: | 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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