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This paper deals with the discrete system being the finite-differenceapproximation of the Sturm-Liouville problem with frozen argument. The inverseproblem theory is developed for this discrete system. We describe the twoprincipal cases: degenerate and non-degenerate. For these two cases,appropriate inverse problems statements are provided, uniqueness theorems areproved, and reconstruction algorithms are obtained. Moreover, the relationshipbetween the eigenvalues of the continuous problem and its finite-differenceapproximation is investigated. We obtain the "correction terms" forapproximation of the discrete problem eigenvalues by using the eigenvalues ofthe continuous problem. Relying on these results, we develop a numericalalgorithm for recovering the potential of the Sturm-Liouville operator withfrozen argument from a finite set of eigenvalues. The effectiveness of thisalgorithm is illustrated by numerical examples.

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