Cite this article as:

Efremova L. S. Numerical Solution of Inverse Spectral Problems for Sturm–Liouville Operators with Discontinuous Potentials . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 3, pp. 273-279. DOI: https://doi.org/10.18500/1816-9791-2014-14-3-273-279

Language: 
Russian
Heading: 
Mathematics
UDC: 
517.984

Numerical Solution of Inverse Spectral Problems for Sturm–Liouville Operators with Discontinuous Potentials

Authors: 
Efremova Liubov Sergeevna, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , liubov.efremova@gmail.com
Abstract: 

We consider Sturm–Liouville differential operator with potential having a finite number of simple discontinuities. This paper is devoted to the numerical solution of such inverse spectral problems. The main result of this work is a procedure that is able to recover both the points of discontinuities as well as the heights of the jumps. Following, using these results, we may apply a suitable numerical method (for example, the generalized Rundell–Sacks algorithm with a special form of the reference potential) to reconstruct the potential more precisely.

Key words: 
Sturm–Liouville differential operator, inverse spectral problem, discontinuous potential, numerical solution.
DOI: 
https://doi.org/10.18500/1816-9791-2014-14-3-273-279
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