A numerical resolution of the Gelfand-Levitan equation
type: Item
instance of: scholarly article
title: A numerical resolution of the Gelfand-Levitan equation
zbMATH Open document ID: 0859.65138
DOI: 10.1016/0377-0427(95)00275-8
author: Bui Doan Khanh
published in: Journal of Computational and Applied Mathematics
publication date: 1996-11-13T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 81U40
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34L25
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 932482
zbMATH Keywords: Gelfand-Levitan equation
zbMATH Keywords: inverse scattering
zbMATH Keywords: inverse Sturm-Liouville problem
zbMATH Keywords: Fredholm integral equations
zbMATH Keywords: predictor-corrector scheme
zbMATH Keywords: numerical examples
reviewed by: Lechoslaw Hącia
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00275-8
OpenAlex ID: W1974096367
cites work: A computation of Fermi-Dirac integrals by asymptotics and the Hermite corrector formula
cites work: Numerical solution of the Gel'fand-Levitan equation
cites work: Reflectionless Transmission through Dielectrics and Scattering Potentials
cites work: Q3997293
cites work: Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
cites work: An Example of the Effect of Rescaling of the Reflection Coefficient on the Scattering Potential for the One-Dimensional Schrodinger Equation
cites work: Inverse scattering—exact solution of the Gel’fand-Levitan equation
description: scientific article; zbMATH DE number 932482