• Bulletin of the Korean Mathematical Society
• /
• 제44권3호
• /
• pp.439-445
• /
• 2007

The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $$x_{n+1}={\frac{Ax_{n-1}}{B+Cx_{n-2}{\iota}x_{n-2k}$$, n = 0, 1, 2,..., where A, B, C are nonnegative real numbers and $\iota$, k are nonnegative in tegers, $\iota{\leq}k$.

• Journal of applied mathematics & informatics
• /
• 제25권1_2호
• /
• pp.269-282
• /
• 2007

In this paper, we consider a two-dimensional fractional space-time diffusion equation (2DFSTDE) on a finite domain. We examine an implicit difference approximation to solve the 2DFSTDE. Stability and convergence of the method are discussed. Some numerical examples are presented to show the application of the present technique.

• Journal of applied mathematics & informatics
• /
• 제25권1_2호
• /
• pp.375-382
• /
• 2007

We Study, firstly, the dynamics of the difference equation $x_{n+1}\;=\;{\alpha}\;+\;{\frac{x^p_n}{x^p_{n-1}}}$, with $p\;{\in}\;(0,\;1)\;and\;{\alpha}\;{\in}\;[0,\;{\infty})$. Then, we generalize our results to the (k + 1)th order difference equation $x_{n+1}\;=\;{\alpha}\;+\;{\frac{x^p_n}{nx^p_{n-k}}$, $k\;=\;2,\;3,\;{\cdots}$ with positive initial conditions.

• Journal of the Chungcheong Mathematical Society
• /
• 제27권2호
• /
• pp.173-181
• /
• 2014

In this paper, using the definition and properties of frequency measurement, we describe the properties of solutions of a difference equation as the initial value belongs to different intervals of the whole domain. We get the main result that if the initial value belongs to [-1, 1] which is different from $\frac{-1{\pm}\sqrt{5}}{2}$, then the solution defined by initial value have two frequent limits 0 and 1 of the same degree 0.5.

• The Pure and Applied Mathematics
• /
• 제11권1호
• /
• pp.15-22
• /
• 2004

In this paper, we investigate asymptotic stability, oscillation, asymptotic behavior and existence of the period-2 solutions for difference equation $x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$ where ${\alpha}\;{\geq}\;0,\;{\beta}\;>\;0.\;$\mid$p$\mid$\;{\geq}\;1$, and the initial conditions $x_{-1}\;and\;x_0$ are arbitrary positive real numbers.

• Journal of applied mathematics & informatics
• /
• 제8권1호
• /
• pp.45-57
• /
• 2001

A parametric scheme is proposed for the numerical solution of the nonlinear Boussinesq equation. The numerical method is developed by approximating the time and the space partical derivatives by finite-difference re placements and the nonlinear term by an appropriate linearized scheme. The resulting finite-difference method is analyzed for local truncation error and stability. The results of a number of numerical experiments are given for both the single and the double-soliton wave. AMS Mathematics Subject Classification : 65J15, 47H17, 49D15.

• Korean Journal of Mathematics
• /
• 제18권3호
• /
• pp.299-309
• /
• 2010

In this paper, we study the first order nonlinear neutral difference equation: $${\Delta}(x(n)+px(n-{\tau}))+f(n,x(n-c),x(n-d))=r(n),\;n{\geq}n_0$$. Using the Banach fixed point theorem, we prove the existence of bounded positive solutions of the equation, suggest Mann iterative schemes of bounded positive solutions, and discuss the error estimates between bounded positive solutions and sequences generated by Mann iterative schemes.

• Journal of applied mathematics & informatics
• /
• 제29권3_4호
• /
• pp.879-889
• /
• 2011

In this paper, we investigate the local asymptotic stability, the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation $x_{n+1}=\frac{a+bx_nx_{n-k}}{A+Bx_n+Cx_{n-k}}$, n = 0, 1,${\ldots}$, where the parameters a, b, A, B, C and the initial conditions $x_{-k}$, ${\ldots}$, $x_{-1}$, $x_0$ are positive real numbers.

• Journal of Information Processing Systems
• /
• 제14권5호
• /
• pp.1068-1074
• /
• 2018

In this paper, we consider the delay partial differential equation of three dimensions with constant coefficients. We established the alternating direction difference scheme by the standard finite difference method, gave the order of convergence of the format and the expression of the difference scheme truncation errors.

• Kyungpook Mathematical Journal
• /
• 제56권2호
• /
• pp.507-516
• /
• 2016

In this paper, we introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation $$x_{n+1}={\frac{ax_{n-3}}{b-cx_{n-1}x_{n-3}}}$$, $n=0,1,{\ldots}$ where a, b, c are positive real numbers and the initial conditions $x_{-3}$, $x_{-2}$, $x_{-1}$, $x_0$ are real numbers.