Finite-difference approximation of the inverse Sturm–Liouville problem with frozen argument

This paper deals with the discrete system being finite-difference approximation of Sturm–Liouville problem frozen argument. The inverse theory is developed for this system. We describe two principal cases: degenerate and non-degenerate. For these cases, appropriate problems statements are provided, uniqueness theorems proved, reconstruction algorithms obtained. Moreover, relationship between eigenvalues continuous its investigated. obtain “correction terms” by using problem. Relying on results, we develop a numerical algorithm recovering potential operator argument from finite set eigenvalues. effectiveness illustrated examples.