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On hypersingular integrals

On hypersingular integrals
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Singular difference integrals, hypersingular integrals and their applications

Singular difference integrals, hypersingular integrals and their applications
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Direct Evaluation of Hypersingular Galerkin Surface Integrals

SIAM Journal of Scientific Computing, 2004
Summary: A direct algorithm for evaluating hypersingular integrals arising in a three-dimensional Galerkin boundary integral analysis is presented. The singular integrals are defined as limits to the boundary, and by integrating two of the four dimensions analytically, the coincident integral is shown to be divergent.
T Kaplan
exaly   +3 more sources

On a method of calculation of hypersingular integrals

Russian Mathematics, 2016
Hypersingular integrals, defined as finite part of divergent integrals by Hadamard, generalize singular integrals in the sense of the main Cauchy value and they are used both in theoretic problems and in applications, as mechanics, electrodynamics, aerodynamics, acoustics, \dots In this paper, conditions to calculate hypersingular integrals of kind \[ \
I V Boikov
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Rough Bilinear Hypersingular Integrals

Potential Analysis, 2022
The main purpose of this paper is to establish the boundedness of bilinear hypersingular integrals with rough kernels. The main theorem in this paper is an extension of Grafakos, He, and Honzik's main result in [\textit{L. Grafakos} and \textit{R. H. Torres}, Adv. Math. 165, No. 1, 124--164 (2002; Zbl 1032.42020)]. It is a generalization of the Leibniz
Cui, Yige, Liu, Honghai, Si, Zengyan, Wang, Hanbin   +3 more
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Hypersingular Integral Equations in Computational Electrodynamics

Computational Mathematics and Modeling, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Davydov, A. G., Zakharov, E. V., Pimenov, Yu. V.   +2 more
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Asymptotic error expansions for hypersingular integrals

Advances in Computational Mathematics, 2011
The authors consider the hypersingular integral \[ I(g)=f.p.\displaystyle\int_{a}^{b}\frac{g(x)}{|x-t|^{1+\alpha}}dx ...
Jin Huang 0011, Zhu Wang 0003, Rui Zhu
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Numerical Integration Formulas for Hypersingular Integrals

Numerical Mathematics: Theory, Methods and Applications
Summary: It is known that the solution of the Cauchy problem for partial differential equations of hyperbolic type can be reduced to singular integrals of a unique form. Laterly, singular integrals were called integrals in the sense of Hadamard or Hadamard integrals. In addition to equations of the hyperbolic type, Hadamard integrals are widely used in
Shadimetov, Kholmat M., Akhmedov, Dilshod M.   +1 more
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A Gauss quadrature rule for hypersingular integrals

Applied Mathematics and Computation, 2007
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Samir A. Ashour, Hany M. Ahmed
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Asymptotic Expansions for Two-Dimensional Hypersingular Integrals

Numerische Mathematik, 2005
Following the ideas from the authors' earlier paper [ibid. 81, 273--291 (1998; Zbl 0932.41027)], they obtain variants of the classicsl Euler-Maclaurin expansion for some two-dimensional integrals. The constant term in the expansion provides the value of Hadamard finite-part integral and by this way, the purposed expansion may be used for the numerical ...
LYNESS J. N, MONEGATO, Giovanni
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