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T. MacRobert (1955)
Higher Transcendental FunctionsNature, 175
Galina Rasolko, S. Sheshko (2020)
An approximate solution of one singular integro-differential equation using the method of orthogonal polynomials
G. Rasol’ko, S. Sheshko, M. Sheshko (2019)
Numerical Method for Some Singular Integro-Differential EquationsDifferential Equations, 55
(1983)
Vychislitel’nye primeneniya mnogochlenov i ryadov Chebysheva (Computational Applications of Chebyshev Polynomials and Series)
I. Meleshko, P. Lasyi (2011)
Approximate solution of one singular integro-differential equationRussian Mathematics, 55
Галина Расолько (2019)
To the numerical solution of singular integro-differential Prandtl equation by the method of orthogonal polynomialsJournal of the Belarusian State University. Mathematics and Informatics
(1984)
Metod singulyarnykh integral'nykh uravnenii v dvumernykh zadachakh difraktsii (Method of Singular Integral Equations in Two-dimensional Diffraction Problems)
(1953)
Translated under the title: Vysshie transtsendentnye funktsii
We consider a mathematical model of scattering of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$H$$\end{document}-polarized electromagnetic waves by a screen with acurvilinear boundary based on a singular integro-differential equation with a Cauchy kernel and alogarithmic singularity. The integrands contain both the unknown function and its first derivative.For the numerical analysis of this model, two computational schemes are constructed based on therepresentation of the unknown function in the form of a linear combination of orthogonalChebyshev polynomials and spectral relations, which permit one to obtain simple analyticalexpressions for the singular component of the equation. The expansion coefficients of the solutionin terms of the basis of Chebyshev polynomials are calculated as a solution of the correspondingsystem of linear algebraic equations. The results of numerical experiments show that the error inthe approximate solution on a grid of 20–30 nodes does not exceed the roundoff error.
Differential Equations – Springer Journals
Published: Jul 8, 2021
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