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Journal of the Belarusian State University. Mathematics and Informatics, 2018, Volume 3, Pages 68–74
(Mi bgumi121)
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This article is cited in 3 scientific papers (total in 3 papers)
Computational Mathematics
Numerical solution of singular integro-differential Prandtl equation by the method of orthogonal polynomials
G. A. Rasolko Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
Abstract:
The paper is constructed and proved computational scheme for a solution of singular Prandtl of integro-differential equations with singular integral over the interval of the real axis, understood in the sense of the Cauchy principal value. This equation reduces to the equivalent Fredholm equation of the second kind by inversion of the singular integral in the class of functions unbounded at the ends and the application of spectral relations for the singular integral. At the same time we investigate the condition of solvability of a Fredholm integral equation of the second kind with a logarithmic kernel of a special kind. The new computational scheme is based on applying spectral relations for the singular integral to the integral entering into the equivalent equation. Uniform estimates of the errors of approximate solutions are obtained.
Keywords:
integro-differential equation; Prandtl equation; numerical solution; method of orthogonal polynomials.
Received: 18.06.2018
Citation:
G. A. Rasolko, “Numerical solution of singular integro-differential Prandtl equation by the method of orthogonal polynomials”, Journal of the Belarusian State University. Mathematics and Informatics, 3 (2018), 68–74
Linking options:
https://www.mathnet.ru/eng/bgumi121 https://www.mathnet.ru/eng/bgumi/v3/p68
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Abstract page: | 54 | Full-text PDF : | 17 | References: | 16 |
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