• Coupled systems mechanics
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• v.8 no.2
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• pp.129-146
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• 2019

The main goal of this work is to develop a numerical simulator to study an isothermal single-phase two-component flow in a naturally fractured oil reservoir, taking into account advection and diffusion effects. We use the Peng-Robinson equation of state with a volume translation to evaluate the properties of the components, and the discretization of the governing partial differential equations is carried out using the Finite Difference Method, along with implicit and first-order upwind schemes. This process leads to a coupled non-linear algebraic system for the unknowns pressure and molar fractions. After a linearization and the use of an operator splitting, the Conjugate Gradient and Bi-conjugated Gradient Stabilized methods are then used to solve two algebraic subsystems, one for the pressure and another for the molar fraction. We studied the effects of fractures in both the flow field and mass transport, as well as in computing time, and the results show that the fractures affect, as expected, the flow creating a thin preferential path for the mass transport.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.5
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• pp.2403-2407
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• 2012

Finite number of pile elements are considered in load transfer method. And section force and movement of each pile element are computed by considering compatibilities between pile displacement and the load transfer along a pile and between displacement and resistance at the tip of the pile. For the conventional load transfer method, large amount of computations due to iterations are needed. Formulation of finite difference equation from the differential equation which depicts pile behavior under axial loading was accomplished in order to simplify the computation for obtaining pile section forces and displacements. By comparing the results between the simplified computation method and the reported data, there was no difference between the two results.

• Journal of KSNVE
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• v.7 no.1
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• pp.55-60
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• 1997

In order to examine the validity of an asymptotic solution obtained from the method of multiple scales, we investigate a third-order subharmonic resonance response of a bar constrained by a nonlinear spring to a harmonic excitation. The motion of the bar is governed by a linear partial differential equation with a nonlinear boundary condition. The nonlinear boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution.

• Journal of electromagnetic engineering and science
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• v.18 no.3
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• pp.212-214
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• 2018

The finite-difference time-domain (FDTD) model was developed to analyze electromagnetic (EM) wave propagation in an inhomogeneous ionosphere. The EM analysis of ionosphere is complicated, owing to various propagation environments that are significantly influenced by plasma frequency, cyclotron frequency, and collision frequency. Based on the simple auxiliary differential equation (ADE) technique, we present an accurate FDTD algorithm suitable for the EM analysis of complex phenomena in the ionosphere under arbitrary-direction geomagnetic field. Numerical examples are used to validate our FDTD model in terms of the reflection coefficient of a single magnetized plasma slab. Based on the FDTD formulation developed here, we investigate EM wave propagation characteristics in the ionosphere using realistic ionospheric data for South Korea.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.299-312
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• 2008

In this paper, we establish some oscillation criteria for nonautonomous second order neutral delay dynamic equations $(x(t){\pm}r(t)x({\tau}(t)))^{{\Delta}{\Delta}}+H(t,\;x(h_1(t)),\;x^{\Delta}(h_2(t)))=0$ on a time scale ${\mathbb{T}}$. Oscillatory behavior of such equations is not studied before. This is a first paper concerning these equations. The results are not only can be applied on neutral differential equations when ${\mathbb{T}}={\mathbb{R}}$, neutral delay difference equations when ${\mathbb{T}}={\mathbb{N}}$ and for neutral delay q-difference equations when ${\mathbb{T}}=q^{\mathbb{N}}$ for q>1, but also improved most previous results. Finally, we give some examples to illustrate our main results. These examples arc [lot discussed before and there is no previous theorems determine the oscillatory behavior of such equations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.61-74
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• 2014

This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.49-65
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• 2006

A robust numerical method for a singularly perturbed second-order ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.73-80
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• 2006

In order to examine the validity of an asymptotic solution for nonlinear interaction in asymmetric vibration modes of a perfect circular plate, we obtain the numerical solution. The motion of the plate is governed by nonlinear partial differential equation. The initial and boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution. It is found that traveling waves relating clockwise and counterclockwise as well as standing wave are depicted by the numerical solution.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1285-1304
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• 2010

The purpose of this paper is to establish some sufficient conditions for oscillation of solutions of the second-order functional dynamic equation of Emden-Fowler type $\[a(t)x^{\Delta}(t)\]^{\Delta}+p(t)|x^{\gamma}(\tau(t))|\|x^{\Delta}(t)\|^{1-\gamma}$ $sgnx(\tau(t))=0$, $t\;{\geq}\;t_0$, on a time scale $\mathbb{T}$, where ${\gamma}\;{\in}\;(0,\;1]$, a, p and $\tau$ are positive rd-continuous functions defined on $\mathbb{T}$, and $lim_{t{\rightarrow}{\infty}}\;{\tau}(t)\;=\;\infty$. Our results include some previously obtained results for differential equations when $\mathbb{T}=\mathbb{R}$. When $\mathbb{T}=\mathbb{N}$ and $\mathbb{T}=q^{\mathbb{N}_0}=\{q^t\;:\;t\;{\in}\;\mathbb{N}_0\}$ where q > 1, the results are essentially new for difference and q-difference equations and can be applied on different types of time scales. Some examples are worked out to demonstrate the main results.

• Steel and Composite Structures
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• v.27 no.6
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• pp.777-788
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• 2018

An investigation on the thermal buckling resistance of simply supported FGM beams having parabolic-concave thickness variation and temperature dependent material properties is presented in this paper. An analytical formulation based on the first order beam theory is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. a function of thickness variation is introduced which controls the parabolic variation intensity of the beam thickness without changing its original material volume. The results showed the high importance of taking into account the temperature-dependent material properties in the thermal buckling analysis of such critical beam sections. Different Influencing parametric on the thermal stability are studied which may help in design guidelines of such complex structures.