Results 31 to 40 of about 1,234,888 (203)

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

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

Pell Equation. IV. Fastest algorithm for solving the Pell equation

Pell Equation. IV. Fastest algorithm for solving the Pell equation
application/pdf 紀要論文 The fastest algorithm for solving the Pell equations, x^2-Dy^2=1 (called Pell-1) and x^2-Dy^2=-1 (Llep-1) , are demonstrated with two typical examples. The essence of the algorithm is i) to obtain the periodic continued fraction expression for the square root of D, ii) to prepare four caterpillar graphs by using the terms derived ...
70940, Hosoya, haruo
openaire   +2 more sources

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

Generalized Pell Equations for 2 × 2 Matrices

Discussiones Mathematicae - General Algebra and Applications, 2017
In this paper we consider the solutions of the generalized matrix Pell equations X2 − dY2 = cI, where X and Y are 2 × 2 matrices over ℤ, d is a non-zero (positive or negative) square-free integer, c is an arbitrary integer and I is the 2 × 2 identity ...
Cohen Boaz
doaj   +1 more source

On the sequences of $(q,k)$-generalized Fibonacci numbers [PDF]

Mathematica Bohemica
We consider a new family of recurrence sequences, the $(q,k)$-generalized Fibonacci numbers. These sequences naturally extend the well-known sequences of $k$-generalized Fibonacci numbers and generalized $k$-order Pell numbers.
Jean Lelis, Gersica Freitas, Alessandra Kreutz, Elaine Silva   +3 more
doaj   +1 more source