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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 1, Pages 3–9
DOI: https://doi.org/10.7868/S0044466915010020 (Mi zvmmf10130) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Finite-difference proof of the completeness of eigenfunctions of the Sturm–Liouville operator in conservative form

A. R. Alievab, E. Kh. Eyvazova

a Faculty of Applied Mathematics and Cybernetics, Baku State University, ul. Z. Khalilova 23, Baku, AZ1148, Azerbaijan
b Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, ul. B. Vakhabzade 9, Baku, AZ1141, Azerbaijan
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DOI: https://doi.org/10.7868/S0044466915010020
Abstract: A finite-difference method is used to prove the completeness of the eigenfunctions of the Sturm–Liouville operator in conservative form. The finite-difference schemes corresponding to the conservative Sturm–Liouville equation with various boundary conditions are shown to be self-adjoint. The accuracy and convergence of the method are analyzed, and the properties of eigenvalues and eigenvectors of the difference scheme approximating the differential equation and the boundary conditions are examined.
Key words: Sturm–Liouville operator, finite-difference method, self-adjoint finite-difference schemes, completeness of eigenfunctions.
Received: 10.04.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 1, Pages 1–7
DOI: https://doi.org/10.1134/S0965542515010029
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: A. R. Aliev, E. Kh. Eyvazov, “Finite-difference proof of the completeness of eigenfunctions of the Sturm–Liouville operator in conservative form”, Zh. Vychisl. Mat. Mat. Fiz., 55:1 (2015), 3–9; Comput. Math. Math. Phys., 55:1 (2015), 1–7
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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