Discontinuous inverse Strum-Liouville problems with symmetric potentials
Technical Report
·
OSTI ID:5046499
In this paper we study the Inverse Sturm-Liouville problem on a finite interval with a symmetric potential function with two interior discontinuities. In the introductory chapter we survey previous results on the existence and uniqueness of solutions to inverse Sturm-Liouville problems and discuss earlier numerical methods. We present a uniqueness proof for the inverse Sturm-Liouville problem on a finite interval with a symmetric potential having two interior jump discontinuities. We show that any absolutely continuous function can be expanded in terms of the eigenfunctions of a Sturm-Liouville problem with two discontinuities. We consider two Sturm-Liouville problems with different symmetric potentials with two discontinuities satisfying symmetric boundary conditions and symmetric jump conditions. We find that if only a finite number of eigenvalues differ then a simple expression for the difference of the potentials can be established. In addition, the locations of the discontinuities are uniquely determined. Finally, we derive an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically and present the results of numerical experiments.
- Research Organization:
- Lawrence Berkeley Lab., CA (USA)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 5046499
- Report Number(s):
- LBL-24974; ON: DE88009803
- Country of Publication:
- United States
- Language:
- English
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