Department of Mathematics
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A Rayleigh–Ritz Method for Numerical Solutions of Linear Fredholm Integral Equations of the Second Kind
Kaya, Ruşen; Taşeli, Hasan (2022-01-01)
A Rayleigh–Ritz Method is suggested for solving linear Fredholm integral equations of the second kind numerically in a desired accuracy. To test the performance of the present approach, the classical one-dimensional Schröd...
Singular inverse Sturm-Liouville problems with Hermite pseudospectral methods
Altundag, H.; Taşeli, Hasan (2021-10-01)
A numerical approximation to recover certain symmetric potentials in the singular inverse Sturm-Liouville problems over (-infinity,infinity) is presented. A Hermite pseudospectral method is employed to cope with the corres...
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...
The Laguerre Pseudospectral Method for the M Dimensional Radial Schrödinger Equation
ALICI, HAYDAR; Taşeli, Hasan (2013-09-07)
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 (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...
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