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On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals
AbstractThis paper is devoted to constructing quadrature formulas for evaluating singular and hypersingular integrals. For evaluating integrals with...
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Existence of Hypersingular Integrals with a Power Singularity of Arbitrary Integer Order
AbstractThe existence of a hypersingular integral on an interval with a singularity of arbitrary integer order is considered. It is shown that the...
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Method of Boundary Integral Equations with Hypersingular Integrals in Boundary-Value Problems
In this paper, we formulate mathematical foundations of applications of boundary integral equations with strongly singular integrals understood in...
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Superconvergence of Newton–Cotes rule for computing hypersingular integral on a circle
In this paper, the composite Newton–Cotes rule for evaluating hypersingular integral on a circle is investigated, we focus on the emphasis of the...
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Erratum to: On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals
An Erratum to this paper has been published: https://doi.org/10.1134/S1995423922040115
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On the Solvability of a Hypersingular Integral Equation on a Surface with Isothermal Coordinates
AbstractWe study the solvability of one hypersingular integral equation on a smooth surface with boundary under the assumption that there exist...
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Boundary Hypersingular Integral Delay Equation for Nonstationary Problems of Scattering by Perfectly Conducting Bodies
AbstractWe consider the application of the method of boundary integral equations to the problem of scattering of an electromagnetic field obeying...
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The convergence rate of truncated hypersingular integrals generated by the modified Poisson semigroup
Hypersingular integrals have appeared as effective tools for inversion of multidimensional potential-type operators such as Riesz, Bessel, Flett,...
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A radial integration displacement discontinuity method with discontinuous isoparametric elements for 3D fracture simulations
To improve the accuracy of displacement discontinuity method and enhance its adaptivity, a general-purpose 3D displacement discontinuity method with...
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Modification of the Discrete Singularity Method for Nonuniform Grids As Applied to One-Dimensional Integral Equations with a Strong Singularity in the Kernel
AbstractFormulas are constructed for the approximate calculation of one-dimensional singular and hypersingular integrals over an interval with an...
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Cubic spline quadrature rule to calculate supersingular integral on interval
The cubic spline quadrature rule for the calculation of supersingular integral (also called “third order hypersingular integral”) is discussed. The...
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Dynamic Instability of Shallow Shells Interacting with a Three-Dimensional Potential Gas Flow
To study the interaction of a vibrating shallow shell with a three-dimensional subsonic gas flow, we deduce a system of hypersingular integral...
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Boundary Integrals for Data Reconstruction on an Elastostatic Crack
The elastostatic Cauchy problem of fracture mechanics is studied in a two-dimensional bounded domain containing a crack. Given Cauchy data on the...
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Hypersingular Integrals in Integral Equations and Inequalities: Fundamental Review Study
The present review deals with the fundamental approaches that cover the numerical solutions of singular and hypersingular integrals. The contribution...