Results 71 to 80 of about 909 (183)

Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials

Mathematics, 2018
This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials.
Taekyun Kim, Dae San Kim, Jongkyum Kwon, Dmitry V. Dolgy   +3 more
doaj   +1 more source

Some generalized Jacobi polynomials

Computers & Mathematics with Applications, 2003
Following the work of the first author [Int. J. Math. Math. Sci. 24, No. 10, 673--689 (2000; Zbl 0967.33006)] in this paper the authors obtain the explicit expressions for the coefficients in the three term pure recurrence relation for generalized Jacobi polynomials defined by a positive weight function which involves a \(p\)th power of \((1-x)\).
Atia, M.J., Alaya, J., Ronveaux, A.
openaire   +2 more sources

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9814-9831, June 2026.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source

On Saigo Fractional $q$-Calculus of a General Class of $q$-Polynomials [PDF]

Sahand Communications in Mathematical Analysis
In this paper, we derive Saigo fractional $q$-integrals of the general class of $q$-polynomials and demonstrate their application by investigating $q$-Konhouser biorthogonal polynomial,  $q$-Jacobi polynomials and basic analogue of the Kamp$\acute{e}$ de
Biniyam Shimelis, Dayalal Suthar
doaj   +1 more source

Chebyshev Smoothing With Adaptive Block‐FSAI Preconditioners for the Multilevel Solution of Higher‐Order Problems With the Partition of Unity Method

Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.
ABSTRACT In this paper, we assess the performance of adaptive and nested factorized sparse approximate inverses as smoothers in multilevel V‐cycles, when smoothing is performed following the Chebyshev iteration of the fourth kind, for the efficient solution of linear systems arising from a conforming discretization of higher‐order partial differential ...
Pablo Jiménez Recio, Marc Alexander Schweitzer   +1 more
wiley   +1 more source

Riemann–Liouville Operator in Weighted L_p Spaces via the Jacobi Series Expansion

Axioms, 2019
In this paper, we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann−Liouville fractional integral and derivative operators on a compact of the real axis.
Maksim V. Kukushkin
doaj   +1 more source

An Augmented Lagrangian Preconditioner for Navier–Stokes Equations With Runge–Kutta in Time

Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.
ABSTRACT We consider an implicit Runge–Kutta method for the numerical time integration of the nonstationary incompressible Navier–Stokes equations. This yields a sequence of nonlinear problems to be solved for the stages of the Runge–Kutta method. The resulting nonlinear system of differential equations is discretized using a finite element method.
Santolo Leveque, Yunhui He, Maxim Olshanskii   +2 more
wiley   +1 more source

A new family of orthogonal polynomials in three variables

Journal of Inequalities and Applications, 2020
In this paper we introduce a six-parameter generalization of the four-parameter three-variable polynomials on the simplex and we investigate the properties of these polynomials.
Rabia Aktaş, Iván Area, Esra Güldoğan   +2 more
doaj   +1 more source

An upper bound on Jacobi polynomials

Journal of Approximation Theory, 2007
Let ${\bf P}_k^{(α, β)} (x)$ be an orthonormal Jacobi polynomial of degree $k.$ We will establish the following inequality \begin{equation*} \max_{x \in [δ_{-1},δ_1]}\sqrt{(x- δ_{-1})(δ_1-x)} (1-x)^α(1+x)^β ({\bf P}_{k}^{(α, β)} (x))^2 < \frac{3 \sqrt{5}}{5}, \end{equation*} where $δ_{-1}
openaire   +3 more sources

Jacobi polynomials method for a coupled system of Hadamard fractional Klein–Gordon–Schrödinger equations

Alexandria Engineering Journal
In this work, the Caputo-type Hadamard fractional derivative is utilized to introduce a coupled system of time fractional Klein–Gordon-Schrödinger equations.
M.H. Heydari, M. Razzaghi
doaj   +1 more source