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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2017, Volume 10, Issue 3, Pages 156–162 (Mi vyuru395)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Notes

Spectral problems on compact graphs

S. I. Kadchenkoab, S. N. Kakushkinb, G. A. Zakirovaa

a South Ural State University, Chelyabinsk, Russian Federation
b Nosov Magnitogorsk State Technical University, Magnitogorsk, Russian Federation

Abstract: The method of finding the eigenvalues and eigenfunctions of abstract discrete semi-bounded operators on compact graphs is developed. Linear formulas allowing to calculate the eigenvalues of these operators are obtained. The eigenvalues can be calculates starting from any of their numbers, regardless of whether the eigenvalues with previous numbers are known. Formulas allow us to solve the problem of computing all the necessary points of the spectrum of discrete semibounded operators defined on geometric graphs. The method for finding the eigenfunctions is based on the Galerkin method. The problem of choosing the basis functions underlying the construction of the solution of spectral problems generated by discrete semibounded operators is considered. An algorithm to construct the basis functions is developed. A computational experiment to find the eigenvalues and eigenfunctions of the Sturm–Liouville operator defined on a two-ribbed compact graph with standard gluing conditions is performed. The results of the computational experiment showed the high efficiency of the developed methods.

Keywords: perturbed operators; eigenvalues; eigenfunctions; compact graph; continuity conditions; Kirchhoff conditions.

DOI: https://doi.org/10.14529/mmp170314

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Bibliographic databases:

UDC: 519.624.3
MSC: 47A10
Received: 21.04.2017
Language:

Citation: S. I. Kadchenko, S. N. Kakushkin, G. A. Zakirova, “Spectral problems on compact graphs”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:3 (2017), 156–162

Citation in format AMSBIB
\Bibitem{KadKakZak17}
\by S.~I.~Kadchenko, S.~N.~Kakushkin, G.~A.~Zakirova
\paper Spectral problems on compact graphs
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2017
\vol 10
\issue 3
\pages 156--162
\mathnet{http://mi.mathnet.ru/vyuru395}
\crossref{https://doi.org/10.14529/mmp170314}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000418233500014}
\elib{http://elibrary.ru/item.asp?id=28922158}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Akhtyamov, Kh. R. Mamedov, E. N. Yilmazoglu, “Boundary inverse problem for star-shaped graph with different densities strings-edges”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 11:3 (2018), 5–17  mathnet  crossref  elib
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