Optimal with respect to accuracy methods for evaluating hypersingular integrals

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2021-12-30 DOI:10.15507/2079-6900.23.202104.360-378

I. Boykov, A. Boykova

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Abstract

In this paper we constructed optimal with respect to order quadrature formulas for evaluating one- and multidimensional hypersingular integrals on classes of functions Ωur,γ(Ω,M), Ω¯ur,γ(Ω,M), Ω=[−1,1]l, l=1,2,…,M=Const, and γ is a real positive number. The functions that belong to classes Ωur,γ(Ω,M) and Ω¯ur,γ(Ω,M) have bounded derivatives up to the rth order in domain Ω and derivatives up to the sth order (s=r+⌈γ⌉) in domain Ω∖Γ, Γ=∂Ω. Moduli of derivatives of the vth order (r

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求超奇异积分的最优精度方法

在本文中，我们构造了在函数类Ωur，γ(Ω，M)， Ω¯ur，γ(Ω，M)， Ω=[−1,1]l, l=1,2，…，M=Const上求一元和多维超奇异积分的最优阶正交公式，并且γ是实数。Ωur的功能属于类,γ(Ω,M)和Ω¯ur,γ(Ω,M)有限域Ω衍生品到仅仅秩序和衍生品的某事秩序(s = r +⌈γ⌉)在域Ω∖Γ,Γ=∂Ω。v阶导数(r

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