Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Efremova L. S. Numerical Solution of Inverse Spectral Problems for Sturm–Liouville Operators with Discontinuous Potentials. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 3, pp. 273-279. DOI: 10.18500/1816-9791-2014-14-3-273-279, EDN: SMSJUR

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

Efremova Liubov Sergeevna, Saratov State University

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.

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