Polynomial Spline Approach for Double Integrals with Algebraic Singularity

Eshkuvatov, Zainidin K.; Long, Nik Mohd Asri Nik; Midi, Habshah; Khaldjigitov, Abduvali

doi:10.1088/1742-6596/435/1/012009

Cited by 3 publications

(1 citation statement)

References 10 publications

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“…Eshkuvatov et al [2] constructed Cubature formulas for the evaluation of double integrals (1) on the rectangle with algebraic singularity by replacing the density function h(x, y) with the S Λ (P ) given by (4); a modified spline function interpolation of type (0, 2) . Rate of convergence are obtained in the classes of function h(x, y) ∈ C 2,α (Ω).…”

Section: Introductionmentioning

confidence: 99%

Construction of cubature formula for double integration with algebraic singularity by spline polynomial

Bichi

Eshkuvatov

Long

et al. 2015

2015 International Conference on Research and Education in Mathematics (ICREM7)

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In this note, singular integration problems of the formwhere Ω = [a1, a2] × [b1, b2],x = (x, y) ∈ Ω and fixed point x0 = (x0, y0) ∈ 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 C 2,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.

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Section: Introductionmentioning

confidence: 99%

Construction of cubature formula for double integration with algebraic singularity by spline polynomial

Bichi

Eshkuvatov

Long

et al. 2015

2015 International Conference on Research and Education in Mathematics (ICREM7)

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

Bichi

Eshkuvatov

Long

et al. 2016

AIP Conference Proceedings

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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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The automatic quadrature scheme for the first order weighted singular integrals

Eshkuvatov,

Bakhramov

2023

The 15th Universiti Malaysia Terengganu Annual Symposium 2021 (Umtas 2021)

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Polynomial Spline Approach for Double Integrals with Algebraic Singularity

Cited by 3 publications

References 10 publications

Construction of cubature formula for double integration with algebraic singularity by spline polynomial

Construction of cubature formula for double integration with algebraic singularity by spline polynomial

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

The automatic quadrature scheme for the first order weighted singular integrals

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