Department of Mathematics
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Unification of Stieltjes-Calogero type relations for the zeros of classical orthogonal polynomials
ALICI, HAYDAR; Taşeli, Hasan (2015-09-30)
The classical orthogonal polynomials (COPs) satisfy a second-order differential equation of the form sigma(x)y '' + tau(x)y' + lambda y = 0, which is called the equation of hypergeometric type (EHT). It is shown that two n...
Inverse Sturm-Liouville problems with pseudospectral methods
Altundag, H.; Boeckmann, C.; Taşeli, Hasan (2015-07-03)
In this paper a technique to obtain a first approximation for singular inverse Sturm-Liouville problems with a symmetrical potential is introduced. The singularity, as a result of unbounded domain (-infinity, infinity), is...
The Laguerre pseudospectral method for the radial Schrodinger equation
ALICI, HAYDAR; Taşeli, Hasan (2015-01-01)
By transforming dependent and independent variables, radial Schrodinger equation is converted into a form resembling the Laguerre differential equation. Therefore, energy eigenvalues and wavefunctions of M-dimensional radi...
On the Orthogonality of q-Classical Polynomials of the Hahn Class
Alvarez-Nodarse, Renato; Adiguzel, Rezan Sevinik; Taşeli, Hasan (2012-01-01)
The central idea behind this review article is to discuss in a unified sense the orthogonality of all possible polynomial solutions of the q-hypergeometric difference equation on a q-linear lattice by means of a qualitativ...
Pseudospectral methods for solving an equation of hypergeometric type with a perturbation
Alici, H.; Taşeli, Hasan (Elsevier BV, 2010-06-15)
Almost all, regular or singular, Sturm-Liouville eigenvalue problems in the Schrodinger form
On the special values of monic polynomials of hypergeometric type
Taşeli, Hasan (Springer Science and Business Media LLC, 2008-01-01)
Special values of monic polynomials y(n)(s), with leading coefficients of unity, satisfying the equation of hypergeometric type
The Laguerre pseudospectral method for the reflection symmetric Hamiltonians on the real line
Taşeli, Hasan; Alici, H. (Springer Science and Business Media LLC, 2007-05-01)
Hermite-Weber functions provide a natural expansion basis for the numerical treatment of the Schrodinger equation on the whole real line. For the reflection symmetric Hamiltonians, however, it is shown here that the transf...
A model for the computation of quantum billiards with arbitrary shapes
Erhan, Inci M.; Taşeli, Hasan (Elsevier BV, 2006-10-01)
An expansion method for the stationary Schrodinger equation of a three-dimensional quantum billiard system whose boundary is defined by an arbitrary analytic function is introduced. The method is based on a coordinate tran...
The scaled Hermite–Weber basis in the spectral and pseudospectral pictures
Taşeli, Hasan; Alıcı, H. (Springer Science and Business Media LLC, 2005-10)
Computational efficiencies of the discrete (pseudospectral, collocation) and continuous (spectral, Rayleigh-Ritz, Galerkin) variable representations of the scaled Hermite-Weber basis in finding the energy eigenvalues of Sc...
A class of orthogonal polynomials suggested by a trigonometric Hamiltonian: Antisymmetric states
Taşeli, Hasan (Springer Science and Business Media LLC, 2005-05-01)
This is the second in a series of papers dealing with the sets of orthogonal polynomials generated by a trigonometric Hamiltonian. In the first of this series, a subclass of the Jacobi polynomials denoted by T-n((u)) (x) a...
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