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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {Numerical {Solution} of {Inverse} {Spectral} {Problems} for {Sturm{\textendash}Liouville} {Operators} with {Discontinuous} {Potentials}},
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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/

[1] Levitan B. M., Inverse Sturm–Liouville Problems, VNU Sci. Press, Utrecht, 1987, 240 pp. | MR | MR | Zbl

[2] Marchenko V. A., Sturm–Liouville operators and applications, Birkhäuser, Basel, 1986, 367 pp. | MR | MR | Zbl

[3] Ignatiev M. Yu., Yurko V. A., “Numerical methods for solving inverse Sturm–Liouville problems”, Results in Math., 52 (2008), 63–74 | DOI | MR | Zbl

[4] Rafler M., Böckmann C., “Reconstruction method for inverse Sturm–Liouville problems with discontinuous potentials”, Inverse Problems, 23:3 (2007), 933–946 | DOI | MR | Zbl

[5] Rundell W., Sacks P. E., “Reconstruction techniques for classical inverse Sturm–Liouville problems”, Mathematics of Computation, 58:197 (1992), 161–183 | DOI | MR | Zbl

[6] Freiling G., Yurko V. A., Inverse Sturm–Liouville Problems and Their Applications, NOVA Science Publ., Huntington, N. Y., 2001, 305 pp. | MR | Zbl

[7] Oppenheim A. V., Schafer R. W., Discrete-time Signal Processing, Prentice-Hall, 1975, 585 pp. | Zbl

[8] Vinokurov V. A., Sadovnichii V. A., “Asymptotics of any order for the eigenvalues and eigenfunctions of the Sturm–Liouville boundary-value problem on a segment with a summable potential”, Izvestiya : Mathematics, 64:4 (2000), 695–754 | DOI | DOI | MR | Zbl