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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 8, Pages 1363–1372 (Mi zvmmf9725)  
On the regularization of a class of integral equations of the first kind whose kernels are discontinuous on the diagonals

A. P. Khromov, G. V. Khromova

Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia
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Abstract: For a class of integral equations of the first kind whose kernels are discontinuous on the diagonals, the convergence of the Lavrent'ev regularization method is proved by using methods of the spectral theory of integral operators. These methods lead to a special Dirac system, and finding the asymptotics of fundamental solutions is an important part of the proof.
Key words: integral equation of the first kind, regularization method, involution, convergence, Lavrent'ev method, Dirac system.
Received: 14.03.2012
English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 8, Pages 1079–1088
DOI: https://doi.org/10.1134/S0965542512080064
Bibliographic databases:
Document Type: Article
UDC: 519.642
Language: Russian
Citation: A. P. Khromov, G. V. Khromova, “On the regularization of a class of integral equations of the first kind whose kernels are discontinuous on the diagonals”, Zh. Vychisl. Mat. Mat. Fiz., 52:8 (2012), 1363–1372; Comput. Math. Math. Phys., 52:8 (2012), 1079–1088
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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