Method for solving inverse spectral problems on quantum star graphs
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Publication:6414781
DOI10.1515/JIIP-2022-0045arXiv2210.12500MaRDI QIDQ6414781
Vladislav V. Kravchenko, Sergei Avdonin
Publication date: 22 October 2022
Abstract: A new method for solving inverse spectral problems on quantum star graphs is proposed. The method is based on Neumann series of Bessel functions representations for solutions of Sturm-Liouville equations. The representations admit estimates for the series remainders which are independent of the real part of the square root of the spectral parameter. This feature makes them especially useful for solving direct and inverse spectral problems requiring calculation of solutions on large intervals in the spectral parameter. Moreover, the first coefficient of the representation is sufficient for the recovery of the potential. The method for solving the inverse spectral problem on the graph consists in reducing the problem to a two-spectra inverse Sturm-Liouville problem on each edge. Then a system of linear algebraic equations is derived for computing the first coefficient of the series representation for the solution on each edge and hence for recovering the potential. The proposed method leads to an efficient numerical algorithm that is illustrated by a number of numerical tests.
Sturm-Liouville theory (34B24) Inverse problems involving ordinary differential equations (34A55) Boundary value problems on graphs and networks for ordinary differential equations (34B45)
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