Geodesic
Numerical Solution of Inverse Spectral Problems for Sturm--Liouville Operators with Discontinuous Potentials
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 273-279.

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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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L. S. Efremova. Numerical Solution of Inverse Spectral Problems for Sturm--Liouville Operators with Discontinuous Potentials. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 273-279. http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a4/

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