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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 3, Pages 432–440
DOI: https://doi.org/10.7868/S0044466916030030 (Mi zvmmf10356) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Justification of the Galerkin method for hypersingular equations

S. I. Eminov, V. S. Eminova

Novgorod State University, ul. B. S.-Peterburgskaya 41, Veliky Novgorod, 173003, Russia
Full-text PDF (134 kB) Citations (9)
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DOI: https://doi.org/10.7868/S0044466916030030
Abstract: The paper presents a theoretical study of hypersingular equations of the general form for problems of electromagnetic-wave diffraction on open surfaces of revolution. Justification of the Galerkin is given. The method is based on the separation of the principal term and its analytic inversion. The inverse of the principal operator is completely continuous. On the basis of this result, the equivalence of the initial equation to a Fredholm integral equation of the second kind is proven. An example of numerical solution with the use of Chebyshev polynomials of the second kind is considered.
Key words: hypersingular equations, Galerkin method, justification of the Galerkin method, equations of electromagnetic-wave diffraction.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 3664
Received: 03.12.2012
Revised: 24.08.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 3, Pages 417–425
DOI: https://doi.org/10.1134/S0965542516030039
Bibliographic databases:
Document Type: Article
UDC: 519.642.7
Language: Russian
Citation: S. I. Eminov, V. S. Eminova, “Justification of the Galerkin method for hypersingular equations”, Zh. Vychisl. Mat. Mat. Fiz., 56:3 (2016), 432–440; Comput. Math. Math. Phys., 56:3 (2016), 417–425
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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