Results 71 to 80 of about 110,049 (182)

Studies in Sums of Finite Products of the Second, Third, and Fourth Kind Chebyshev Polynomials

Mathematics, 2020
In this paper, we consider three sums of finite products of Chebyshev polynomials of two different kinds, namely sums of finite products of the second and third kind Chebyshev polynomials, those of the second and fourth kind Chebyshev polynomials, and ...
Taekyun Kim, Dae San Kim, Hyunseok Lee, Jongkyum Kwon   +3 more
doaj   +1 more source

The Numerical Approximation of Caputo Fractional Derivatives of Higher Orders Using a Shifted Gegenbauer Pseudospectral Method: A Case Study of Two-Point Boundary Value Problems of the Bagley–Torvik Type

Mathematics
This paper introduces a novel Shifted Gegenbauer Pseudospectral (SGPS) method for approximating Caputo fractional derivatives (FDs) of an arbitrary positive order.
Kareem T. Elgindy
doaj   +1 more source

Computing with Expansions in Gegenbauer Polynomials

, 2007
. In this work, we develop fast algorithms for computations involving finite expansions in Gegenbauer polynomials. We describe a method to convert a linear combination of Gegenbauer polynomials up to degree n into a representation in a different family ...
Jens Keiner
core  

Fourier–Gegenbauer Integral Galerkin Method for Solving the Advection–Diffusion Equation with Periodic Boundary Conditions

Computation
This study presents the Fourier–Gegenbauer integral Galerkin (FGIG) method, a new numerical framework that uniquely integrates Fourier series and Gegenbauer polynomials to solve the one-dimensional advection–diffusion (AD) equation with spatially ...
Kareem T. Elgindy
doaj   +1 more source

Matrix-valued Gegenbauer polynomials

, 2014
25 pages, accompanying Maple worksheet available at http://www.math.ru.nl/~koelink/publist-ro.html. Proofs have been simplified by exploiting shift operators extensively. The proofs of the symmetry of some matrix-valued differential operators have been simplified using the LDU-decomposition of the weight. The proof of the matrix-valued Pearson equation
Koelink, Erik, Rios, Ana M. de los, Roman, Pablo   +2 more
openaire   +2 more sources

An Integral Formula For Generalized Gegenbauer Polynomials And Jacobi Polynomials

, 2007
The generalized Gegenbauer polynomials are orthogonal polynomials with respect to the weight function jxj . An integral formula for these polynomials is proved, which serves as a transformation between h-harmonic polynomials associated with Z ...
Yuan Xu
core  

A numerical technique for solving multi-dimensional fractional optimal control problems

Journal of Taibah University for Science, 2018
In this article, we use the operation matrix (OM) of Riemann–Liouville fractional integral of the shifted Gegenbauer polynomials with the Lagrange multiplier method to provide efficient numerical solutions to the multi-dimensional fractional optimal ...
Hoda F. Ahmed
doaj   +1 more source

SOME MISCELLANEOUS PROPERTIES FOR GEGENBAUER MATRIX POLYNOMIALS

, 2013
The main aim of this paper is to obtain hypergeometric matrix representations and generating matrix function for the Gegenbauer matrix polynomials.
ÇEKİM, BAYRAM, ALTIN, ABDULLAH
core  

Fractional Jacobi Renormalization Operators for Fixed Classical Orthogonal Polynomial Systems

Fractal and Fractional
For a fixed orthogonal polynomial sequence, classical orthonormalization changes the polynomials by degree-dependent scalar factors. If the polynomials themselves are kept fixed, scalar-measure normalization is usually impossible; on a compact interval ...
Edson Pindza, Hopolang Phillip Mashele
doaj   +1 more source

The Orthogonal Riesz Fractional Derivative

Axioms
The aim of this paper is to extend the concept of the orthogonal derivative to provide a new integral representation of the fractional Riesz derivative. Specifically, we investigate the orthogonal derivative associated with Gegenbauer polynomials Cn(ν)(x)
Fethi Bouzeffour
doaj   +1 more source