Singular inverse Sturm–Liouville problems with Hermite pseudospectral methods
Department of Mathematics, Hitit University, 19030, Çorum, Turkey
2 Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey
Accepted: 24 September 2021
Published online: 10 October 2021
A numerical approximation to recover certain symmetric potentials in the singular inverse Sturm–Liouville problems over is presented. A Hermite pseudospectral method is employed to cope with the corresponding direct problem on the real line, which is encountered in the iterative procedure proposed for the inverse problem. The usual but unwelcome ill-posed structure of the resulting numerical algorithm has been treated to some extent by the help of a flexible optimization parameter and regularization techniques. The construction of some specific potentials are illustrated to emphasize the effectiveness of the present scheme.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021