inverse spectral problem

On Inverse Problem for Differential Operators with Deviating Argument

Authors: Yurko V. A.

Second-order functional differential operators with a constant delay are considered. Properties of their spectral characteristics are obtained, and a nonlinear inverse spectral problem is studied, which consists in constructin goperators from the irspectra. We establish the unique nessand develop a constructive procedure for solution of the inverse problem.

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

Authors: Efremova L. S.

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.