Optimal quadrature formulas for hypersingular integrals in the Sobolev space
Keywords:
optimal quadrature formulas, the extremal function, Sobolev space, optimal coefficients, Hadamard type singular integralAbstract
The solution of the Cauchy problem for partial differential equations of hyperbolic type J. Hadamard led to singular integrals of a special form. Later they 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 the theory of elasticity, electrodynamics, aerodynamics, and a number of other important areas of mechanics and mathematical physics. The exact calculation of the Hadamard integrals is possible only in exceptional cases, so there is a need to develop approximate methods for calculating. In the present paper, we develop an optimal algorithm for the approximate calculation of the Hadamard integral for ???? = 3. Here we are engaged in finding the analytical form of the coefficients of the optimal quadrature formula.
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Copyright (c) 2024 Д.М. Ахмедов, А.Х. Авезов, И.К. Хакимова (Автор)
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