On a method for solving the inverse Sturm–Liouville problem

Author:

Kravchenko Vladislav V.1

Affiliation:

1. Regional Mathematical Center of Southern Federal University , Rostov-on-Don , Russia ; on leave from Cinvestav, Mexico

Abstract

Abstract A method for solving the inverse Sturm–Liouville problem on a finite interval is proposed. It is based on a Fourier–Legendre series representation of the integral transmutation kernel. Substitution of the representation into the Gel’fand–Levitan equation leads to a linear algebraic system of equations and consequently to a simple algorithm for recovering the potential. Numerical illustrations are presented.

Funder

Consejo Nacional de Ciencia y Tecnología

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Reference10 articles.

1. G. Freiling and V. Yurko, Inverse Sturm–Liouville Problems and Their Applications, Nova Science, Huntington, 2001.

2. M. Ignatiev and V. Yurko, Numerical methods for solving inverse Sturm–Liouville problems, Results Math. 52 (2008), no. 1–2, 63–74.

3. D. Jackson, The Theory of Approximation. Reprint of the 1930 Original, American Mathematical Society, Providence, 1994.

4. A. Kammanee and C. Böckmann, Boundary value method for inverse Sturm–Liouville problems, Appl. Math. Comput. 214 (2009), 342–352.

5. V. V. Kravchenko, L. J. Navarro and S. M. Torba, Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions, Appl. Math. Comput. 314 (2017), no. 1, 173–192.

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