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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2015, Volume 19, Number 4, Pages 613–623
DOI: https://doi.org/10.14498/vsgtu1396
(Mi vsgtu1396)
 

Differential Equations and Mathematical Physics

On the solution of the convolution equation with a sum-difference kernel

A. G. Barseghyan

Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan, 0019, Republic of Armenia (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: The paper deals with the integral equations of the second kind with a sum-difference kernel. These equations describe a series of physical processes in a medium with a reflective boundary. It has noted some difficulties at applying the methods of harmonic analysis, mechanical quadrature, and other approaches to approximate solution of such equations. The kernel average method is developed for numerical-analytical solution of considered equation in non singular case. The kernel average method has some similarity with known strip method. It was applied for solution of Wiener-Hopf integral equation in earlier work of the author. The kernel average method reduces the initial equation to the linear algebraic system with Toeplitz-plus-Hankel matrix. An estimate for accuracy is obtained in the various functional spaces. In the case of large dimension of the obtained algebraic system the known methods of linear algebra are not efficient. The proposed method for solving this system essentially uses convolution structure of the system. It combines the method of non-linear factorization equations and discrete analogue of the special factorization method developed earlier by the author to the integral equations.
Keywords: integral equation with a sum-difference kernel, medium with a reflective boundary, kernel average method, factorization.
Funding agency Grant number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia SCS 13-1A271
This work was supported by the State Committee of Science of the Ministry of Education and Science of Republic Armenia, project no. SCS 13–1A271.
Original article submitted 19/XII/2014
revision submitted – 12/V/2015
Bibliographic databases:
Document Type: Article
UDC: 517.968.2
MSC: 45E10
Language: Russian
Citation: A. G. Barseghyan, “On the solution of the convolution equation with a sum-difference kernel”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:4 (2015), 613–623
Citation in format AMSBIB
\Bibitem{Bar15}
\by A.~G.~Barseghyan
\paper On the solution of the convolution equation with~a~sum-difference kernel
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2015
\vol 19
\issue 4
\pages 613--623
\mathnet{http://mi.mathnet.ru/vsgtu1396}
\crossref{https://doi.org/10.14498/vsgtu1396}
\zmath{https://zbmath.org/?q=an:06969181}
\elib{https://elibrary.ru/item.asp?id=25687490}
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    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    Full-text PDF :234
    References:82
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