On the Dynamics of a Higher-Order Rational Difference Equation [PDF]
Discrete Dynamics in Nature and Society, 2011 The aim of this paper is to investigate the global asymptotic stability and the periodic character for the rational difference equation xn+1=αxn-1/(β+γΠi=lkxn-2ipi), n=0,1,2,…, where the parameters α,β,γ,pl,pl+1,…,pk are nonnegative real numbers, and l ...
A. M. Ahmed
doaj +3 more sources
Stability of a rational difference equation [PDF]
Applied Mathematics Letters, 2012 We investigate the stability of the solutions of a rational difference equation and confirm the conjectures which were proposed by Kulenović and Ladas in [M.R.S. Kulenović, G.
Zeng, Fanping +3 more
core +6 more sources
On two rational difference equations
Applied Mathematics and Computation, 2006 In this paper, we study the oscillating property of positive solutions and the global asymptotic stability of the unique equilibrium of the two rational difference equations [GRAPHICS] and [GRAPHICS] where a is a nonnegative constant.
Yang, X. +3 more
core +2 more sources
Global behavior of a third order rational difference equation [PDF]
Applied Mathematics and Computation, 2006 summary:In this paper, we determine the forbidden set and give an explicit formula for the solutions of the difference equation $$x_{n+1}=\frac {ax_{n}x_{n-1}}{-bx_{n}+ cx_{n-2}},\quad n\in \mathbb {N}_0 $$ where $a$, $b$, $c$ are positive real numbers ...
Aloqeili, Marwan, Abo-Zeid, Raafat
core +2 more sources
Dynamics of a System of Rational Higher-Order Difference Equation [PDF]
Discrete Dynamics in Nature and Society, 2013 We focus on a system of a rational -order difference equation , , , where . We investigate the dynamical behavior of positive solution for the system.
Banyat Sroysang
doaj +2 more sources
Global Asymptotic Stability for a Fourth-Order Rational Difference Equation [PDF]
Discrete Dynamics in Nature and Society, 2009 Our aim is to investigate the global behavior of the following fourth-order rational difference equation: 𝑥𝑛+1=(𝑥𝑛𝑥𝑛−2𝑥𝑛−3+𝑥𝑛+𝑥𝑛−2+𝑥𝑛−3+𝑎)/(𝑥𝑛𝑥𝑛−2+𝑥𝑛𝑥𝑛−3+𝑥𝑛−2𝑥𝑛−3+1+𝑎), 𝑛=0,1,2,… where 𝑎∈[0,∞) and the initial values
Meseret Tuba Gülpinar, Mustafa Bayram
doaj +2 more sources
Higher-order finite-difference methods for partial differential equations [PDF]
, 1997 This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis develops two families of numerical methods, based upon rational approximations having distinct real poles, for solving first- and second-order ...
Cheema, Tasleem Akhter
core +7 more sources
On linear systems and τ functions associated with Lamé's equation and Painlevé's equation VI. [PDF]
, 2011 Painleve's transcendental differential equation PVI may be expressed as the consistency condition for a pair of linear differential equations with 2 by 2 matrix coefficients with rational entries.
Blower, Gordon
core +5 more sources
Fast computation of the nonlocal boundary condition in finite difference parabolic equation radiowave propagation simulations [PDF]
, 2008 Finite difference parabolic equation method (FD-PEM) codes using a nonlocal boundary condition to model radiowave propagation over electrically large domains, require the computation of time consuming spatial convolution integrals. For the first time, we
Mias, Christos
core +1 more source
Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation [PDF]
, 2008 The Yablonskii-Vorob'ev polynomials yn(t), which are defined by a second order bilinear differential-difference equation, provide rational solutions of the Toda lattice.
Common, Alan K., Hone, Andrew N.W.
core +1 more source