Abstract
We consider the Sturm–Liouville equation on a finite interval with a real-valued integrable potential and propose a method for solving the following general inverse problem. We recover the potential from a given set of the output boundary values of a solution satisfying some known initial conditions for a set of values of the spectral parameter. Special cases of this problem include the recovery of the potential from the Weyl function, the inverse two-spectra Sturm–Liouville problem, as well as the recovery of the potential from the output boundary values of a plane wave that interacted with the potential. The method is based on the special Neumann series of Bessel functions representations for solutions of Sturm–Liouville equations. With their aid, the problem is reduced to the classical inverse Sturm–Liouville problem of recovering the potential from two spectra, which is solved again with the help of the same representations. The overall approach leads to an efficient numerical algorithm for solving the inverse problem. Its numerical efficiency is illustrated by several examples.
Funder
Consejo Nacional de Ciencia y Tecnología
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference20 articles.
1. Inverse Sturm—Liouville problem with analytical functions in the boundary condition;Bondarenko;Open Math.,2020
2. Solvability and stability of the inverse Sturm–Liouville problem with analytical functions in the boundary condition;Bondarenko;Math. Methods Appl. Sci.,2020
3. Inverse spectral analysis with partial information on the potential, III. Updating boundary conditions;Gesztesy;Int. Math. Res. Notices,1997
4. Inverse spectral problems and closed exponential systems;Ann. Math.,2005
5. Yurko, V.A. (2007). Introduction to the Theory of Inverse Spectral Problems, Fizmatlit.
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献