Geodesic
Algorithms for calculating the eigenvalues of initial-boundary value problems for a wave differential equation set in a graph with varying edges
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 4, pp. 29-34 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper develops algorithms for calculating the eigenvalues of initial-boundary value problems for a wave differential equation set in a star graph with time-varying edge lengths. The change of variables helped to reduce the considered spectral problems to initial-boundary value problems with fixed edges. The obtained formulas were used to find eigenvalues for a wave differential equation set in a star graph with time-varying edges with any ordinal numbers. The formulas for calculating the eigenvalues will allow developing algorithms for solving inverse spectral problems set in quantum graphs with varying edges.
Keywords: eigenvalues and eigenfunctions; discrete and self-conjugate operators; regularized trace method; Galerkin method. 
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S. I. Kadchenko; L. S. Ryazanova. Algorithms for calculating the eigenvalues of initial-boundary value problems for a wave differential equation set in a graph with varying edges. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 4, pp. 29-34. http://geodesic.mathdoc.fr/item/VYURM_2024_16_4_a3/

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