Numerical analogue of the Gelfand-Levitan on a finite interval.

Abstract

Gelfand and Levitan in their celebrated article in 1951, and later Gasymov and Levitan in 1964 have shown that a monotone increasing function is a spectral function of a singular Sturm-Liouville problem on a half-line in the limit point case at infinity if and only if it satisfies an existence and a smoothness condition. In this paper we consider discrete Sturm Liouville eigenvalue problem. Determined numerical the spectral data of the operator and the auxiliary function. To find the numerical values of the kernel of Sturm Liouville problem is solved Fredholm integral equation of the second kind.