Geodesic
Properties of finite-difference analog of one-dimensional Laplace operator on the graph
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2012), pp. 52-59

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The finite-difference analogs of one-dimensional Laplace operator on the graph-star and the graph with a cycle are considered. At the same time differential operator characteristic continuity at its reduction to the finite-difference analog is essential: the structure of an eigenvalue set is similar to the structure of a proper value set of a differential operator, completeness of eigenvectors in the finite-dimensional space remains, the finite-difference analog of Laplace operator remains symmetric and positive.
Keywords: one-dimensional Laplace operator, finite-difference analog of Laplace operator, characteristics of operator. 
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     title = {Properties of finite-difference analog of one-dimensional {Laplace} operator on the graph},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {52--59},
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     number = {1},
     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/VSPUI_2012_1_a6/}
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O. A. Makhinova. Properties of finite-difference analog of one-dimensional Laplace operator on the graph. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2012), pp. 52-59. http://geodesic.mathdoc.fr/item/VSPUI_2012_1_a6/