Geodesic
Algorithms for calculating eigenvalues of second order parabolic differential operators on quantum star graphs with time-varying edges
Journal of computational and engineering mathematics, Tome 11 (2024) no. 4, pp. 3-13.

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This paper develops algorithms for calculating the eigenvalues of partial differential operators on star graphs with time-varying edges. The obtained analytical formulas allow finding the eigenvalues of such operators of the required order at a given time. Numerical experiments on calculating the eigenvalues of the problems under study are carried out in the Maple mathematical environment. The calculations performed show the high computational efficiency of the developed method. Using the analytical formulas for calculating the eigenvalues of the operators under consideration obtained in the paper, it is possible to develop algorithms for solving inverse spectral problems for operators on quantum graphs with time-varying edges.
Keywords: graphs, eigenvalues and eigenfunctions, discrete and self-adjoint operators, regularized trace method, Galerkin method. 
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     author = {S. I. Kadchenko and L. S. Ryazanova},
     title = {Algorithms for calculating eigenvalues of second order parabolic differential operators on quantum star graphs with time-varying edges},
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S. I. Kadchenko; L. S. Ryazanova. Algorithms for calculating eigenvalues of second order parabolic differential operators on quantum star graphs with time-varying edges. Journal of computational and engineering mathematics, Tome 11 (2024) no. 4, pp. 3-13. http://geodesic.mathdoc.fr/item/JCEM_2024_11_4_a0/