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 Num. Meth. Prog., 2016, Volume 17, Issue 3, Pages 204–211 (Mi vmp828)

Solution of a model inverse spectral problem for the Sturm–Liouville operator on a graph

N. F. Valeeva, Yu. V. Martynovab, Ya. T. Sultanaevc

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
b RN-UfaNIPIneft Company
c Bashkir State Pedagogical University, Ufa

Abstract: A model inverse spectral problem for the Sturm–Liouville operator on a geometric graph is studied. This problem consists in finding $N$ parameters of the boundary conditions using its $N$ known eigenvalues. It is shown that the problem under consideration possess the property of a monotonic dependence of its eigenvalues on the parameters of the boundary conditions. This problem is reduced to a multiparameter inverse spectral problem for the operator in a finite-dimensional space. A new algorithm for the numerical solution of this problem is proposed.

Keywords: spectral theory of differential operators, geometric graph, Sturm–Liouville operator, spectral problems.

Full text: PDF file (191 kB)
UDC: 517.4+519.71

Citation: N. F. Valeev, Yu. V. Martynova, Ya. T. Sultanaev, “Solution of a model inverse spectral problem for the Sturm–Liouville operator on a graph”, Num. Meth. Prog., 17:3 (2016), 204–211

Citation in format AMSBIB
\Bibitem{ValMarSul16} \by N.~F.~Valeev, Yu.~V.~Martynova, Ya.~T.~Sultanaev \paper Solution of a model inverse spectral problem for the Sturm--Liouville operator on a graph \jour Num. Meth. Prog. \yr 2016 \vol 17 \issue 3 \pages 204--211 \mathnet{http://mi.mathnet.ru/vmp828}