Open AccessQuadrature formulas for Cauchy-type integrals with the Cauchy kernel to a integer power and a Jacobi weight function with complex exponents
Author(s) -
H.A. Amirjanyan,
A.V. Sahakyan,
A K Kukudzhanov
Publication year - 2022
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2231/1/012020
Subject(s) - mathematics , weight function , cauchy distribution , mathematical analysis , quadrature (astronomy) , numerical integration , gaussian quadrature , pure mathematics , nyström method , integral equation , electrical engineering , engineering
The paper presents quadrature formulas for hypersingular integrals of various orders. It is assumed that the density of these integrals is represented as a product of a function that satisfies the Hölder condition and a weight function of Jacobi orthogonal polynomials. In this case, the exponents of the weight function can be complex numbers, the real part of which is greater than -1. Numerical analysis of the dependence of the root-mean-square deviation of the quadrature formula of order 8 on the value of the hypersingular integral calculated using standard software packages is carried out for various complex values of the weight function exponents. For hypersingular integrals up to the fourth order inclusive, a numerical analysis of the convergence of quadrature formulas is carried out for certain complex values of the exponents of the weight function.