• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.441-452
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• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• Steel and Composite Structures
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• v.19 no.3
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• pp.679-695
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• 2015

A numerical solution using finite difference method to evaluate the thermal buckling of simply supported FGM plate with variable thickness is presented in this research. First, the governing differential equation of thermal stability under uniform temperature through the plate thickness is derived. Then, the governing equation has been solved using finite difference method. After validating the presented numerical method with the analytical solution, the finite difference formulation has been extended in order to include variable thickness. The accuracy of the finite difference method for variable thickness plate has been also compared with the literature where a good agreement has been found. Furthermore, a parametric study has been conducted to analyze the effect of material and geometric parameters on the thermal buckling resistance of the FGM plates. It was found that the thickness variation affects isotropic plates a bit more than FGM plates.

• Journal of Korea Soil Environment Society
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• v.5 no.1
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• pp.3-12
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• 2000

The multi-region model, to describe preferential flow, is an equation representing solute transport in soils by dividing soil into numerous pore groups and using the hydraulic properties of the soil. As the model partial differential equation (PDE) is solved numerically with finite difference methods. a modified equivalent partial differential equation(MEPDE) of the partial differential equation of the multi-region model is derived to analyze the accuracy and consistency of the solution of the model PDE and the Von Neumann method is used to analyze the stability of the finite difference scheme. The evaluation obtained from the MEPDE indicated that the finite difference scheme was found to be consistent with the model PDE and had the second order accuracy The stability analysis is performed to analyze the model PDE with the amplification ratio and the phase lag using the Von Neumann method. The amplification ratio of the finite difference scheme gave non-dissipative results with various Peclet numbers and yielded the most high values as the Peclet number was one. The phase lag showed that the frequency component of the finite difference scheme lagged the true solution. From the result of the stability analysis for the model PDE, it is analyzed that the model domain should be discretized in the range of Pe < 1.0 and Cr < 2.0 to obtain the more accurate solution.

• Journal of Korean Society of Forest Science
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• v.88 no.2
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• pp.142-148
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• 1999

This research describes the construction of a site index equation and curves for Douglas-fir plantation (Pseudotsuga menziesii Mirb. Franco) in Nelson, New Zealand. The data sets of 146 Permanent Sample Plots (PSP) were used to build the model, and it was developed using the difference equation method. Parameter estimates were obtained using the non-linear routine of the SAS, PROC NLIN procedure. Of the models tested, a variant of the Schumacher polymorphic yield function showed the higher precision of fitting. About 95% of the observations used to fit the model could be predicted within ${\pm}1.2m$ of the actual values. Therefore, polymorphic family of site index curves, which reflect different shapes for the different site index classes, were derived from the Schumacher equation. It was found that the polymorphic site index equation was more accurate than the anamorphic equation in this study.

• The Journal of the Korea Contents Association
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• v.11 no.12
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• pp.357-363
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• 2011

The aim of this study is to compare radiation dose in diagnostic X-ray radiography and calculated by different mathematical equation. The result of ESDs direct measurement and that calculated by Mori NDD-M shows the biggest difference. On the other hand, equation by Edmonds shows the lowest difference of ESDs. Also, Rectification due to the difference between direct dose measurement and calculation method commutated three-phase, single phase and inverter type, show less difference in the drive way. In conclusion, this study can be helpful for expecting radiation dose-exposure and control exposure parameters for the diagnostic x-ray radiography.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1921-1930
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• 2018

We consider a functional difference equation and use fixed point theory to obtain necessary and sufficient conditions for the asymptotic stability of its zero solution. At the end of the paper we apply our results to nonlinear Volterra infinite delay difference equations.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.269-282
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• 2005

We study the global asymptotic stability, global attractivity, boundedness character, and periodic nature of all positive solutions and all negative solutions of the difference equation $$x_{n+1}\;=\;{\alpha}-{\frac{x_{n-1}}{x_{n}},\;n=0,1,\;{\cdots}$$, where ${\alpha}\;\in\; R$ is a real number, and the initial conditions $x_{-1},\;x_0$ are arbitrary real numbers.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.843-848
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• 2014

In this paper, we investigate the boundedness character, the periodic character and the global behavior of positive solutions of the difference equation $$x_{n+1}=p_n+\frac{x_n}{x_{n-1}},\;n=0,1,{\cdots}$$ where $\{p_n\}$ is a two periodic sequence of nonnegative real numbers and the initial conditions $x_{-1}$, $x_0$ are arbitrary positive real numbers.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.249-262
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• 2014

In this paper, we have developed a non-homogeneous q-difference equation of first order for the generalized Mock theta function of order eight and besides these established limiting case of Mock theta functions of order eight. We have also established identities for Partial Mock theta function and Mock theta function of order eight and provided a number of cases of the identities.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.603-616
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• 2020

In the paper, we establish the validity of the weighted discrete and integral Hardy inequalities with periodic weights and find the best possible constants in these inequalities. In addition, by applying the established discrete Hardy inequality to a certain second-order difference equation, we discuss some oscillation and nonoscillation results.