A numerical resolution of the Gelfand-Levitan equation (Q1923454)

The Gelfand-Levitan equation is the fundamental equation in inverse scattering theory, especially in connection with the inverse Sturm-Liouville problem. This problem is reduced to solving a family of Fredholm integral equations. In this paper, the finite integrals are approximated by the Hermite corrector formula and then solving the considered equation is reduced to a family of linear systems, which are solved by a predictor-corrector scheme. Two numerical examples are presented.