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The transmutation operator method for efficient solution of the inverse Sturm‐Liouville problem on a half‐line
Author(s) -
Delgado Briceyda B.,
Khmelnytskaya Kira V.,
Kravchenko Vladislav V.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5854
Subject(s) - mathematics , legendre polynomials , mathematical analysis , algebraic equation , fourier series , kernel (algebra) , inverse problem , operator (biology) , series (stratigraphy) , inverse , nuclear transmutation , fourier transform , algebraic number , nonlinear system , pure mathematics , geometry , physics , paleontology , biochemistry , chemistry , repressor , quantum mechanics , biology , transcription factor , neutron , gene
The inverse Sturm‐Liouville problem on a half‐line is considered. With the aid of a Fourier‐Legendre series representation of the transmutation integral kernel and the Gel'fand‐Levitan equation, the numerical solution of the problem is reduced to a system of linear algebraic equations. The potential q is recovered from the first coefficient of the Fourier‐Legendre series. The resulting numerical method is direct and simple. The results of the numerical experiments are presented.