Results 21 to 30 of about 661 (172)

Markov Triples with Generalized Pell Numbers

Mathematics, 2023
For an integer k≥2, let (Pn(k))n be the k-generalized Pell sequence which starts with 0,…,0,1 (k terms), and each term afterwards is given by Pn(k)=2Pn−1(k)+Pn−2(k)+⋯+Pn−k(k). In this paper, we determine all solutions of the Markov equation x2+y2+z2=3xyz,
Julieth F. Ruiz, Jose L. Herrera, Jhon J. Bravo   +2 more
doaj   +1 more source

Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular Kernel

Journal of Function Spaces, 2022
This article focuses on finding the numerical solution of the nonlinear time–fractional partial integro–differential equation. For this purpose, we use the operational matrices based on Pell polynomials to approximate fractional Caputo derivative ...
M. Taghipour, H. Aminikhah
doaj   +1 more source

A numerical approach to solve hyperbolic telegraph equations via Pell–Lucas polynomials

Journal of Taibah University for Science, 2023
In this article, a collocation approximation is investigated for approximate solutions of hyperbolic telegraph partial differential equations (HTPDEs). The method is based on evenly spaced collocation points and Pell–Lucas polynomials (PLPs). The form of
Şuayip Yüzbaşı, Gamze Yıldırım
doaj   +1 more source

Explicit algebraic solution of Zolotarev's First Problem for low-degree polynomials

Journal of Numerical Analysis and Approximation Theory, 2019
E.I. Zolotarev's classical so-called First Problem (ZFP), which was posed to him by P.L. Chebyshev, is to determine, for a given \(n\in{\mathbb N}\backslash\{1\}\) and for a given \(s\in{\mathbb R}\backslash\{0\}\), the monic polynomial solution \(Z ...
Heinz Joachim Rack, Robert Vajda
doaj   +7 more sources

On $k$-Pell numbers which are sum of two Narayana's cows numbers [PDF]

Mathematica Bohemica
For any positive integer $k\geq2$, let $(P_n^{(k)})_{n\geq2-k}$ be the $k$-generalized Pell sequence which starts with $0,\cdots,0,1$ ($k$ terms) with the linear recurrence P_n^{(k)} = 2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)}\quad\text{for} n\
Kouèssi Norbert Adédji, Mohamadou Bachabi, Alain Togbé   +2 more
doaj   +1 more source

Pell-Lucas polynomials for numerical treatment of the nonlinear fractional-order Duffing equation

Demonstratio Mathematica, 2023
The nonlinear fractional-order cubic-quintic-heptic Duffing problem will be solved through a new numerical approximation technique. The suggested method is based on the Pell-Lucas polynomials’ operational matrix in the fractional and integer orders.
El-Sayed Adel Abd Elaziz
doaj   +1 more source

Balances in the Set of Arithmetic Progressions

Axioms, 2021
This article focuses on searching and classifying balancing numbers in a set of arithmetic progressions. The sufficient and necessary conditions for the existence of balancing numbers are presented.
Chan-Liang Chung, Chunmei Zhong, Kanglun Zhou   +2 more
doaj   +1 more source

Solution of certain Pell equations [PDF]

Asian-European Journal of Mathematics, 2018
Let [Formula: see text] be any positive integers such that [Formula: see text] and [Formula: see text] is a square free positive integer of the form [Formula: see text] where [Formula: see text] and [Formula: see text] The main focus of this paper is to find the fundamental solution of the equation [Formula: see text] with the help of the continued ...
Zahid Raza, Hafsa Masood Malik
openaire   +3 more sources

Three Diophantine equations concerning the polygonal numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Many authors investigated the problem about the linear combination of two polygonal numbers being a perfect square, i.e., the Diophantine equation mPₖ(x)+nPₖ(y)=z², where Pₖ(x) denotes the x-th k-polygonal number and m, n are positive integers.
Yong Zhang, Mei Jiang, Qiongzhi Tang
doaj   +1 more source

Numerical Solutions via Shifted Pell Polynomials for Third-Order Rosenau–Hyman and Gilson–Pickering Equations

Mathematics
This paper introduces a collocation algorithm for numerically solving the third-order Gilson–Pickering equation (GPE) and the classical Rosenau–Hyman equation (RHE). We employ newly developed shifted Pell polynomials as basis functions.
Mohamed A. Abdelkawy, Waleed Mohamed Abd-Elhameed, Seham S. Alzahrani, Ahmed Gamal Atta, Anjan Biswas   +4 more
doaj   +1 more source