• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. 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. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.7
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• pp.995-1006
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• 2003

The suitability of high-order accurate, centered and upwind-biased compact difference schemes for large eddy simulation is evaluated by a dynamic analysis. Large eddy simulation of isotropic turbulence is performed with various dissipative and non-dissipative schemes to investigate the effect of numerical dissipation on the resolved solutions. It is shown by the present dynamic analysis that upwind schemes reduce the aliasing error and increase the finite differencing error. The existence of optimal upwind scheme that minimizes total numerical error is verified. It is also shown that the finite differencing error from numerical dissipation is the leading source of numerical errors by upwind schemes. Simulations of a turbulent channel flow are conducted to show the existence of the optimal upwind scheme.

• Journal of The Korean Astronomical Society
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• v.34 no.4
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• pp.271-273
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• 2001

We present a 4-parameter implicit Lagrangean code which satisfies conservation of mass, linear and angular momenta, energy and entropy simultaneously. The primary advantage of this scheme is possibility to control dissipative properties of the scheme avoiding the effects of numerical viscosity.

• East Asian mathematical journal
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• v.40 no.1
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• pp.109-118
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• 2024

This paper proposes a numerical method based on domain decomposition to find approximate solutions for one-dimensional convection-diffusion equations with Neumann boundary conditions. First, the equations are transformed into convection-diffusion equations with Dirichlet conditions. Second, the author introduces the Prediction/Correction Domain Decomposition (PCDD) method and estimates errors for the interface prediction scheme, interior scheme, and correction scheme using known error estimations. Finally, the author compares the PCDD algorithm with the fully explicit scheme (FES) and the fully implicit scheme (FIS) using three examples. In comparison to FES and FIS, the proposed PCDD algorithm demonstrates good results.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.21 no.7
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• pp.805-814
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• 2010

The Crank-Nicolson isotropic-dispersion finite difference time domain(CN ID-FDTD) scheme is proposed based on isotropic-dispersion finite difference(ID-FD) $equation^{[1],[2]}$. The dispersion relation of CN ID-FDTD is derived for lossy media by solving the eigenvalue problem of iteration matrix in spatial spectral domain, in addition, the weighting factors and scaling factors of the CN ID-FDTD scheme are presented for low dispersion error. The CN ID-FDTD scheme makes the dispersion error drastically reduced and shows accurate numerical results compared to the conventional Crank-Nicolson FDTD method.

• Journal of Communications and Networks
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• v.7 no.4
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• pp.462-470
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• 2005

We propose a multi-rate and multi-BEP transmission scheme using adaptive overlapping pulse-position modulator (OPPM) and optical power controller in optical code division multiple access (CDMA) networks. The proposed system achieves the multi-rate and multi-BEP transmission by accommodating users with different values of OPPM parameter and transmitted power in the same network. The proposed scheme has advantages that the system is not required to change the code length and number of weight depending on the required bit rate of a user and the difference of bit rates does not have so much effect on the bit error probabilities (BEPs). Moreover, the difference of transmitted powers does not cause the change of bit rate. We analyze the BEPs of the four multimedia service classes corresponding to the com­binations of high/low-rates and low/high-BEPs and show that the proposed scheme can easily achieve distinct differentiation of the service classes with the simple system configuration.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.527-535
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• 2005

Numerical differentiation is one of the main topics which have been studied by many researchers. If we use the forward difference scheme or the centered difference scheme, the convergence rates to the derivative are O(h) and O($h^2$), respectively. In this paper, using the Lagrange Interpolation, we construct a simple high order numerical differentiation scheme which has the convergence rate O($h^{2k}$) if we have 2k+1 equally spaced nodes. Our scheme is constructive.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.623-641
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• 2021

In this paper, numerical treatment of singularly perturbed parabolic delay differential equations is considered. The considered problem have small delay on the spatial variable of the reaction term. To treat the delay term, Taylor series approximation is applied. The resulting singularly perturbed parabolic PDEs is solved using Crank Nicolson method in temporal direction with non-standard finite difference method in spatial direction. A detail stability and convergence analysis of the scheme is given. We proved the uniform convergence of the scheme with order of convergence O(N^-1 + (∆t)²), where N is the number of mesh points in spatial discretization and ∆t is mesh length in temporal discretization. Two test examples are used to validate the theoretical results of the scheme.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.10
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• pp.54-63
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• 2007

To measure water levels from remote cites using a narrowband channel, this paper developed a difference image based JPEG communication scheme and a water level measurement scheme using the sparsely sampled images in time domain. In the slave system located in the field, the images are compressed using JPEG after changed to difference images, among which in a period of data collection those showing larger changes are sampled and transmitted. To measure the water level from the images received in the master system which may contain noises caused by various sources, the averaging scheme and Gaussian filter are used to reduce the noise effects and the Y axis profile of an edge image is used to read the water level. Considering the wild condition of the field, a simplified camera calibration scheme is also introduced. The implemented slave system was installed at a river and its performance has been tested with the data collected for a month.

• 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.