• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.485-502
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• 2015

A computational method for solving singularly perturbed boundary value problem of differential equation with shift arguments of mixed type is presented. When shift arguments are sufficiently small (o(ε)), most of the existing method in the literature used Taylor's expansion to approximate the shift term. This procedure may lead to a bad approximation when the delay argument is of O(ε). The main idea for this work is to deal with constant shift arguments, which are independent of ε. In the present method, we construct the formally asymptotic solution of the problem using the method of composite expansion. The reduced problem is solved numerically by using operator compact implicit method, and the second problem is solved analytically. Error estimate is derived by using the maximum norm. Numerical examples are provided to support the theoretical results and to show the efficiency of the proposed method.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.166-171
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• 2000

A two-dimensional/axisymmetric CSCM upwind flux difference splitting Wavier-Stokes method has been developed to study the finite rate chemically react-ing invisicd and viscous hypersonic flows over blunt-body. A upwind method was chosen due to its robustness in capturing the strong bow shock waves. For the nonequilibrium chemically reacting air, NS-I species conservation equations were strongly coupled with flowfield equations through convection and species production terms. The nonequilibrium wall pressure and heat transfer rate distributions along the vehicle were compared with those from equilibrium and perfect gas calculations. The nonequilibrium species distribution shows the reduced concentrations of O and N species when compared with equilibrium species distribution. The solutions resolved strong bow shock waves md heat transfer rate very accurately when compared with central difference schemes.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.213-217
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• 2005

In this study the water including sediment is assumed that the density is different from fresh water. And the phenomenon inhaled by low pressure around the pipe is numerically simulated in two dimension. The simulation is done using finite difference method in rectangular staggered mesh system and Navier-Stokes equations and continuty equation are employed as governing equations. The method of Irregular leg lengths and stars are adopted to satisfy boundary condition of body boundary. Marker-Density method is used to calculate the density of mixed flow. Also SGS turbulence model is applied to consider vortex smaller then grid at high Renolds number. This study is to analyze inhalation phenomenon of mixed flow with sediment and to verify the numerical method for mixed flow. To verify the numerical results are compared with experimental results

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.88-93
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• 1998

Since rattling noise, which occur in mechanical linkage with free play or glove boxes in passenger cars, play an important role in the generation of industrial noise and vibration, it is interest to study these dynamics. A difference equations are derived which described the motions of a mass constrained by pre-compressed spring and forced by a high frequency base excitation. Two types of saddle are founded from these difference equations and the stable and unstable manifolds are constructed in these saddle point. For a certain region in a parameter space of exciting displacement and coefficient of restitution, transversal intersections of stable and unstable manifolds exist. Therefore it is founded that there are large families of periodic and irregular non-periodic motions in rattling system i.e. chaos motion is observed.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2004.11a
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• pp.221-231
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• 2004

A kinetic theory analysis is made of low-speed gas flows in a microfluidic system consisted of three microchannels in series. The Boitzmann equation simplified by a collision model is solved by means of a finite difference approximation with the discrete ordinate method. For the evaluation of the present method results are compared with those from the DSMC method and an analytical solution of the Navier-Stokes equations with slip boundary conditions. Calculations are made for flows at various Knudsen numbers and pressure ratios across the channel. The results compared well with those from the DSMC method. It is shown that the analytical solution of the Navier-Stokes equations with slip boundary conditions which is suited fur fully developed flows can give relatively good results. In predicting the geometrically complex flows up to a Knudsen number of about 0.06. It is also shown that the present method can be used to analyze extremely low-speed flow fields for which the DSMC method is Impractical.

• Journal of Korea Technology Innovation Society
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• v.4 no.2
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• pp.157-171
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• 2001

This paper discusses the economics of local loop architecture focusing on existing technologies, ADSL, HFC, and new one, PLC, and suggests a new modeling approach of access network system and the numerical equations. To modelize access network system and drive the numerical equations, we consider the double star and the tree & branch architecture and made block diagram of each access system. In addition, we introduce the density of subscriber as a variable and the equation of seeking the optimal number of cell in a service area. The economics of local loop architecture is analyzed in two ways, i.e. with and without consideration of the cost of cable and infrastructure. From the numerical analysis, we find that in case of not including the cost of cable and infrastructure, there is no much difference in the cost per one subscriber, while, in case of including it, there is remarkable difference among technologies. Therefore we conclude that the economics of local loop architecture is depend on the density of subscriber and existing network infrastructures.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.23-31
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• 2008

In this paper, we investigate nonoscillatory solutions of a class of higher order neutral nonlinear difference equations with positive and negative coefficients $\Delta^m(x(n)+p(n)x(\tau(n)))+f_1(n,x(\sigma_1(n)))-f_2(n,x(\sigma_2(n)))=0,\;n{\geq}n_0$. Some sufficient conditions for the existence of nonoscillatory solutions are obtained.

• Korea-Australia Rheology Journal
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• v.16 no.4
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• pp.227-233
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• 2004

Simplified model of slide-fed curtain coating flow has been developed and tested in this study. It rests on the sheet profile equations for curtain thickness in curtain flow and its trajectory derived by the integral momentum balance approach of Higgins and Scriven (1979) and Kistler (1983). It also draws on the film profile equation of film thickness variation in flow down a slide. The equations have been solved in finite difference approximation by Newton iteration with continuation. The results show that how inertia (Rey­nolds number), surface tension (capillary number), inclination angle of the slide, and air pressure difference across the curtain affect sheet trajectory and thickness profile. It has been revealed that approximate models can be useful to easily analyze coating flow dynamics without complex computations, giving qualitative agreement with full theory and with experiment.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.279-294
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• 2013

We are interested in an adaptive grid method for hyperbolic equations. A multiresolution analysis, based on a biorthogonal family of interpolating scaling functions and lifted interpolating wavelets, is used to dynamically adapt grid points according to the physical field profile in each time step. Traditional finite-difference schemes with fixed stencils produce high oscillations around sharp discontinuities. In this paper, we hybridize high-resolution schemes, which are suitable for capturing singularities, and apply a finite-difference approach to the scaling functions at non-singular points. We use a total variation diminishing Runge-Kutta method for the time integration. The computational cost is proportional to the number of points present after compression. We provide several numerical examples to verify our approach.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.67-82
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• 2006

In this paper, we present a finite difference method for the implementation of the rotation of a circular cylinder in the incompressible flow field by solving the two-dimensional unsteady Navier-Stokes equations. The approach is to use staggered grid method so that the accuracy and order of convergence of the associated algorithms can be maintained. The proposed method is easy to be implemented and is effective. A set of simulations for the flow dynamics is provided to show the computational results.