• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.299-306
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• 2008

Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations, which discribe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^\infty$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.51-61
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• 2018

In this article, we mainly use Nevanlinna theory to investigate some special difference equations of malmquist type such as $f^2+({\Delta}_cf)^2={\beta}^2$, $f^2+({\Delta}_cf)^2=R$, $f{^{\prime}^2}+({\Delta}_cf)^2=R$ and $f^2+(f(z+c))^2=R$, where ${\beta}$ is a nonzero small function of f and R is a nonzero rational function respectively. These discussions extend one related result due to C. C. Yang et al. in some sense

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.29-40
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• 2009

Motivated by [Linear Algebra and its Appl. 420(2007), 218-227] and [Linear Algebra and its Appl. 425(2007), 171-183], we, in this paper, study the solvability of periodic boundary value problems of higher order nonlinear functional difference equations with p-Laplacian. Sufficient conditions for the existence of at least one solution of this problem are established.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.127-144
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• 2005

In this paper, we consider the higher order nonlinear neutral delay difference equation of the form $\Delta^{\gamma}(x_{n}+px_{n-\gamma})+f(n, x_{n-\sigma_1(n)}, x_{n-\sigma_2(n)}, \ldots, x_{n-\sigma{_m}(n)})=0$. We give an integrated classification of nonoscillatory solutions of the above equation according to their asymptotic behaviours. Necessary and sufficient conditions for the existence of nonoscillatory solutions with designated asymptotic properties are also established.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.3
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• pp.201-215
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• 2018

In this paper we consider a class of singularly perturbed system of delay differential equations of convection diffusion type with integral boundary conditions. A finite difference scheme on an appropriate piecewise Shishkin type mesh is suggested to solve the problem. We prove that the method is of almost first order convergent. An error estimate is derived in the discrete maximum norm. Numerical experiments support our theoretical results.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.173-183
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• 2003

In this paper, we give a classification of nonoscillatory solution of a second-order neutral delay difference equation of the form △²(x/sub n/-c/sub n/x/sub n-r/)=f(n, x/sub g1(n)/, …, x/sub gm(n)/). Some existence results for each kind of nonoscillatory solutions we also established.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.579-594
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• 2005

In this paper, we will establish some new oscillation criteria for the second-order half-linear delay difference equation $${\Delta}(Pn ({\Delta}Xn)^{\gamma})+q_nx_\array{{\gamma}\\n-{\sigma}}=0,\;n{\geq}n_0$$, where ${\gamma}>0$ is a quotient of odd positive integers. Our results in this paper are sharp and improve some of the well known oscillation results in the literature. Some examples are considered to illustrate our main results.

• International Journal of Safety
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• v.1 no.1
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• pp.13-17
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• 2002

A new system of equations governing the nonlinear thin laminated plates with large deflections using von Karman equations is derived. The effects of transverse shear in the thin interlayer are included as part of the analysis. The finite difference method is used to perform the geometrically nonlinear behavior of the plate. The resultant equations permit the analysis of the effect of transverse shear stress deformation on the overall behavior of the interlayer using the load incremental method. For the purpose of feasibility and validity of this present method, the numerical results are compared with other available solutions for accuracy as well as efficiency. The solution techniques have been implemented and the numerical results of example problem are discussed and evaluated.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.301-319
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• 2020

In this paper, we show that the system of difference equations $x_n={\frac{ay^p_{n-1}+b(x_{n-2}y_{n-1})^{p-1}}{cy_{n-1}+dx^{p-1}_{n-2}}}$, $y_n={\frac{{\alpha}x^p_{n-1}+{\beta}(y_{n-2}x_{n-1})^{p-1}}{{\gamma}x_{n-1}+{\delta}y^{p-1}_{n-2}}}$, n ∈ ℕ₀ where the parameters a, b, c, d, α, β, γ, δ, p and the initial values x-2, x-1, y-2, y-1 are real numbers, can be solved. Also, by using obtained formulas, we study the asymptotic behaviour of well-defined solutions of aforementioned system and describe the forbidden set of the initial values. Our obtained results significantly extend and develop some recent results in the literature.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.401-409
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• 2010

In this paper, we introduce an iterative method to study oscillatory properties of delay difference equations of the following form ${\nabla}_{\alpha}\;[x(t)\;-\;r(t)x(t\;-\;k)]\;+\;p(t)x(t\;-\;{\tau})\;-\;q(t)x(t\;-\;{\sigma})\;=\;0$, $t\;{\geq}\;t_0$, where $t_0\;{\in}\;\mathbb{R}$, t varies in the real interval ($t_0,\;{\infty}$), $\alpha$ > 0, $\kappa$, $\tau$, ${\sigma}\;{\geq}\;0$, $r\;{\in}\;C\;([t_0-{\alpha},\;{\infty}),\;\mathbb{R}^+$, p, $q\;{\in}\;C\;([t_0,\;{\infty}),\;\mathbb{R}^+)$ and ${\nabla}_{\alpha}x(t)\;=\;x(t)\;-\;x(t\;-\;{\alpha})$ for $t\;{\geq}\;t_0$.