• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1001-1015
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• 2009

In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a small parameter multiplying the highest derivative. We prove that the schemes are almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and its derivative are established. Numerical results are provided to illustrate the theoretical results.

• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.99-105
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• 1997

A finite-difference method based on conservative supra characteristic method type upwind flux difference splitting has been developed to study the nonequilibrium chemically reacting inviscid flow. For nonequilibrium air, NS-1 species equations were strongly coupled with flowfield equations through convection and species production terms. Inviscid nonequilibrium chemically reacting air mixture flows over Blunt-body were solved to demonstrate the capability of the current method. At low altitude flight conditions the nonequilibrium air models predicted almost the same temperature, density and pressure behind the shock as equilibrium flow: however, at high altitudes they showed substantial differences due to nonequilibrium chemistry effect. The new nonequilibrium chemically reacting upwind flux difference splitting mettled can be extended to viscous flow and multi-dimensional flow conditions.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.2 no.2
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• pp.197-205
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• 1998

The purpose of this paper is to analyze the electromagnetic field characteristics of array antenna with the finite difference-time domain algorithm. Finite difference equations of Maxwell's equations are defined in cylindrical coordinate systems. To simulate the unbounded problem like a free space, the Mur's absorbing boundary condition is also used. After modeling the array antenna with the grid structure, the transient response of the field distribution is depicted in the time domain.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.335-350
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• 2016

Based on the notion of $q_k$-derivative introduced by the authors in [17], we prove in this paper existence and uniqueness results for nonlinear second-order impulsive $q_k$-difference equations with anti-periodic boundary conditions. Two results are obtained by applying Banach's contraction mapping principle and Krasnoselskii's fixed point theorem. Some examples are presented to illustrate the results.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.329-341
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• 2021

In this study, we consider an efficient and accurate finite difference method for the four underlying asset equity-linked securities (ELS). The numerical method is based on the operator splitting method with non-uniform grids for the underlying assets. Even though the numerical scheme is implicit, we solve the system of discrete equations in explicit manner using the Thomas algorithm for the tri-diagonal matrix resulting from the system of discrete equations. Therefore, we can use a relatively large time step and the computation of the ELS option pricing is fast. We perform characteristic computational test. The numerical test confirm the usefulness of the proposed method for pricing the four underlying asset equity-linked securities.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.25-45
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• 2022

In this study, the non-standard finite difference method for the numerical solution of singularly perturbed parabolic reaction-diffusion subject to Robin boundary conditions has presented. To discretize temporal and spatial variables, we use the implicit Euler and non-standard finite difference method on a uniform mesh, respectively. We proved that the proposed scheme shows uniform convergence in time with first-order and in space with second-order irrespective of the perturbation parameter. We compute three numerical examples to confirm the theoretical findings.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1471-1479
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• 2013

In this paper, we study the non-existence of finite order entire solutions of nonlinear differential-difference of the form $$f^n+Q(z,f)=h$$, where $n{\geq}2$ is an integer, $Q(z,f)$ is a differential-difference polynomial in $f$ with polynomial coefficients, and $h$ is a meromorphic function of order ${\leq}1$.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.883-893
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• 2011

In this paper we study h-stability of the solutions of nonlinear difference system via the notion of $n_{\infty}$-summable similarity between its variational systems. Also, we show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent. Furthermore, we characterize h-stability for nonlinear difference systems by using Lyapunov functions.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.965-968
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• 2005

Roll drafting operation causes variations in the linear density of bundles because the bundle flow cannot be controlled completely by roll pairs. Defects occurring in this operation bring about many problems successively in the next processes. In this paper, we attempt to analyze the draft dynamics and the linear density irregularity based on the governing equation of a bundle motion that has been suggested in our previous studies. For analyzing the dynamic characteristics of the roll drafting operation, it is indispensable to investigate a transient state in time domain before the bundle flux reaches a steady state. However, since governing equations of bundle flow consisting of continuity and motion equations turn out to be nonlinear, and coupled between variables, the solutions for a transient state cannot be obtained by an analytical method. Therefore, we use the Finite Difference Method(FDM), particularly, the FTBS(Forward-Time Backward-Space) difference method. Then, the total equations system yields to an algebraic equations system and is solved under given initial and boundary conditions in an iterative fashion. From the simulation results, we confirm that state variables show different behavior in the transient state; e.g., the velocity distribution in the flow field changes more quickly the linear density distribution. During a transient flow in a drafting zone, the output irregularity is influenced differently by the disturbances, e.g., the variation in input bundle thickness, the drafting speed, and the draft ratio.

• Bulletin of the Society of Naval Architects of Korea
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• v.13 no.1
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• pp.17-23
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• 1976

Some methods of analysis of rectangular plates under distributed load of various intensity with interior supports are presented herein. Analysis of many structures such as bottom, side shell, and deck plate of ship hull and flat slab, with or without internal supports, Floor systems of bridges, included crthotropic bridges is a problem of plate with elastic supports or continuous edges. When the four edges of rectangular plate is simply supported, the double Fourier series solution developed by Navier can represent an exact result of this problem. If two opposite edges are simply supported, Levy's method is available to give an "exact" solution. When the loading condition and supporting condition of a plate does not fall into these cases, no simple analytic method seems to be feasible. Analysis of a simply supported rectangular plate under irregularly distributed loads of various intensity with internal supports is carried out by applying Navier solution well as the "Principle of Superposition." Finite difference technique is used to solve plates under irregularly distributed loads of various intensity with internal supports and with various boundary conditions. When finite difference technique is applied to the Lagrange's plate bending equation, any of fourth order derivative term in this equation produces at least five pivotal points leading to some troubles when the resulting linear algebraic equations are to be solved. This problem was solved by reducing the order of the derivatives to two: the fourth order partial differential equation with one dependent variable, namely deflection, is changed to an equivalent pair of second order partial differential equations with two dependent variables. Finite difference technique is then applied to transform these equations to a set of simultaneous linear algebraic equations. Principle of Superposition is then applied to handle the problems caused by concentrated loads and interior supports. This method can be used for the cases of plates under irregularly distributed loads of various intensity with arbitrary conditions such as elastic supports, or continuous edges with or without interior supports, and this method can also be solve the influence values of deflection, moment and etc. at arbitrary position of plates under the live load.