Geodesic
Algorithms for calculating eigenvalues of discrete semi-bounded operators defined on quantum graphs of star type with variable edges
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 4, pp. 51-65

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The article develops algorithms for calculating the eigenvalues of initial-boundary value problems for differential equations defined on a star graph with variable edges. Numerical experiments on calculating the eigenvalues of the problems under study were carried out in the Maple mathematical environment. The developed technique can be transferred to boundary value problems for any discrete semi-bounded operators and will allow developing algorithms for solving inverse spectral problems defined on quantum graphs with variable edges.
Keywords: graphs, eigenvalues and eigenfunctions, discrete and self-adjoint operators, regularized trace method, Galerkin method. 
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     title = {Algorithms for calculating eigenvalues of discrete semi-bounded operators defined on quantum graphs of star type with variable edges},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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     url = {http://geodesic.mathdoc.fr/item/VYURU_2024_17_4_a4/}
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S. I. Kadchenko; L. S. Ryazanova; I. E. Kadchenko. Algorithms for calculating eigenvalues of discrete semi-bounded operators defined on quantum graphs of star type with variable edges. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 4, pp. 51-65. http://geodesic.mathdoc.fr/item/VYURU_2024_17_4_a4/