Optimal Quadrature Formula for Approximate Calculation of Singular Integrals with Hilbert kernel
Keywords:
singular integral, Hilbert kernel, error functional, optimal quadrature formula, extremal function, differential operator, optimal coefficientsAbstract
Many mathematical models in science and technology have been reduced to the approximate calculation of singular integrals with Cauchy and Hilbert kernels and the approximate solution of integral equations. In this paper, an optimal quadrature formula for approximate calculation of singular integrals with a Hilbert kernel in the Sobolev space is constructed and analytical formulas for coefficients that minimize its error are obtained from among the coefficients of the quadrature formula. For this, the discrete analogue of the second-order differential operator is used. The resulting quadrature formula is exact to a first-order polynomial.
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Copyright (c) 2024 Х.М. Шадиметов, Х.Х. Жабборов (Автор)
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