Open AccessNumerical solution of a weakly singular integral equation by the method of orthogonal polynomials
Author(s) -
С. М. Шешко
Publication year - 2021
Publication title -
žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika/žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika
Language(s) - English
Resource type - Journals
eISSN - 2617-3956
pISSN - 2520-6508
DOI - 10.33581/2520-6508-2021-3-98-103
Subject(s) - mathematics , chebyshev polynomials , orthogonal polynomials , mathematical analysis , chebyshev equation , polynomial , algebraic equation , integral equation , classical orthogonal polynomials , chebyshev nodes , singular integral , jacobi polynomials , logarithm , nonlinear system , physics , quantum mechanics
A scheme is constructed for the numerical solution of a singular integral equation with a logarithmic kernel by the method of orthogonal polynomials. The proposed schemes for an approximate solution of the problem are based on the representation of the solution function in the form of a linear combination of the Chebyshev orthogonal polynomials and spectral relations that allows to obtain simple analytical expressions for the singular component of the equation. The expansion coefficients of the solution in terms of the Chebyshev polynomial basis are calculated by solving a system of linear algebraic equations. The results of numerical experiments show that on a grid of 20 –30 points, the error of the approximate solution reaches the minimum limit due to the error in representing real floating-point numbers.