scholarly journals On convergence of the solutions of the difference equation xn+1=1+xn−1xn

2007 ◽  
Vol 325 (2) ◽  
pp. 1491-1494 ◽  
Author(s):  
Taixiang Sun ◽  
Hongjian Xi
Keyword(s):  
Difference Equation ◽  
The Difference

scholarly journals On Boundedness of Solutions of the Difference Equation xn+1=(pxn+qxn−1)/(1+xn) for q>1+p>1

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Hongjian Xi ◽  
Taixiang Sun ◽  
Weiyong Yu ◽  
Jinfeng Zhao
Keyword(s):  
Difference Equation ◽  
Boundedness Of Solutions ◽  
The Difference

scholarly journals An inequality with application to a difference equation

2004 ◽  
Vol 69 (3) ◽  
pp. 519-528 ◽  
Author(s):  
Jong-Yi Chen ◽  
Yunshyong Chow
Keyword(s):  
Heat Conduction ◽  
Difference Equation ◽  
Heat Conduction Problem ◽  
The Difference

In this paper we shall prove that for any 0 < d ≤ 2, holds for n ≥ 1.As an application, we shall then show that the following recursively defined sequence satisfies The difference equation above originates from a heat conduction problem studied by Myshkis (J. Difference Equ. Appl. 3(1997), 89–91).

On the difference equation

2012 ◽  
Vol 218 (11) ◽  
pp. 6291-6296 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Difference Equation ◽  
The Difference

On the difference equation xn+1=α+βxn−1e−xn

2001 ◽  
Vol 47 (7) ◽  
pp. 4623-4634 ◽  
Author(s):  
H. El-Metwally ◽  
E.A. Grove ◽  
G. Ladas ◽  
R. Levins ◽  
M. Radin
Keyword(s):  
Difference Equation ◽  
The Difference

scholarly journals Analytical Study of the Difference Equation xn+1 = xnxn-6 / xn-5 (±1 – xnxn-6)

2019 ◽  
pp. 1-12
Author(s):  
Abdualrazaq Sanbo ◽  
Elsayed M. Elsayed ◽  
Faris Alzahrani
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Analytical Study ◽  
Initial Conditions ◽  
Specific Form ◽  
Positive Real ◽  
Rational Difference Equations ◽  
Special Cases ◽  
The Difference

This paper is devoted to find the form of the solutions of a rational difference equations with arbitrary positive real initial conditions. Specific form of the solutions of two special cases of this equation are given.

scholarly journals Determination of the number of radicals in the initial chain reactions by mathematical methods

2009 ◽  
Vol 63 (2) ◽  
pp. 121-127
Author(s):  
Branko Pejovic ◽  
Milovan Jotanovic ◽  
Vladan Micic ◽  
Milorad Tomic ◽  
Goran Tadic
Keyword(s):  
General Chemistry ◽  
Difference Equation ◽  
Analytical Form ◽  
Mathematical Methods ◽  
Linear Difference Equations ◽  
Efficient Procedure ◽  
Chain Reactions ◽  
Chemical Equation ◽  
The Difference

Starting from the fact that the real mechanism in a chemical equation takes places through a certain number of radicals which participate in simultaneous reactions and initiate chain reactions according to a particular pattern, the aim of this study is to determine their number in the first couple of steps of the reaction. Based on this, the numbers of radicals were determined in the general case, in the form of linear difference equations, which, by certain mathematical transformations, were reduced to one equation that satisfies a particular numeric series, entirely defined if its first members are known. The equation obtained was solved by a common method developed in the theory of numeric series, in which its solutions represent the number of radicals in an arbitrary step of the reaction observed, in the analytical form. In the final part of the study, the method was tested and verified using two characteristic examples from general chemistry. The study also gives a suggestion of a more efficient procedure by reducing the difference equation to a lower order.

scholarly journals Global Behavior of the Difference Equationxn+1=xn-1g(xn)

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Hongjian Xi ◽  
Taixiang Sun ◽  
Bin Qin ◽  
Hui Wu
Keyword(s):  
Continuous Function ◽  
Difference Equation ◽  
Positive Solution ◽  
Positive Solutions ◽  
Initial Conditions ◽  
Global Behavior ◽  
Initial Values ◽  
The Difference ◽  
Surjective Function

We consider the following difference equationxn+1=xn-1g(xn),n=0,1,…,where initial valuesx-1,x0∈[0,+∞)andg:[0,+∞)→(0,1]is a strictly decreasing continuous surjective function. We show the following. (1) Every positive solution of this equation converges toa,0,a,0,…,or0,a,0,a,…for somea∈[0,+∞). (2) Assumea∈(0,+∞). Then the set of initial conditions(x-1,x0)∈(0,+∞)×(0,+∞)such that the positive solutions of this equation converge toa,0,a,0,…,or0,a,0,a,…is a unique strictly increasing continuous function or an empty set.

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