• 충청수학회지
• /
• 제20권4호
• /
• pp.449-455
• /
• 2007

We obtain a discrete version of a fundamental result by Yoshizawa related to the existence of almost periodic solutions of functional differential equations with finite delay.

• 한국원자력학회:학술대회논문집
• /
• 한국원자력학회 1999년도 춘계학술발표회요약집
• /
• pp.16-16
• /
• 1999

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제12권2호
• /
• pp.69-79
• /
• 2008

Multigrid methods finite element/finite volume methods and their convergence properties are reviewed in a general setting. Some early theoretical results in simple finite element methods in variational setting method are given and extension to nonnested-noninherited forms are presented. Finally, the parallel theory for nonconforming element[13] and for cell centered finite difference methods [15, 23] are discussed.

• 한국정밀공학회지
• /
• 제18권9호
• /
• pp.110-121
• /
• 2001

During hot pipe bending using induction heating, the wall of bending outside is thinned by tensile stress. In design requirement, the reduction of wall thickness is not allowed to exceed 12.5%. So in this study, two methods of bending, one is loading of reverse moment and the other is loading of temperature gradient, have been investigated to design pipe bending process that satisfy design requirements. For this purpose, finite element analysis with a bending radius 2Do(outer diameter of pipe) has been performed to calculate proper reverse moment and temperature gradient to be applied. Induction heating process has been analyzed to estimate influence of heating process parameters on heating characteristic by finite difference method. Then pipe bending experiments have been performed for verification of finite element and finite difference analysis results. Experimental results are in good agreement with the results of simulations.

• 한국도로학회논문집
• /
• 제17권5호
• /
• pp.1-10
• /
• 2015

PURPOSES : A finite difference model considering snow melting process on porous asphalt pavement was derived on the basis of heat transfer and mass transfer theories. The derived model can be applied to predict the region where black-ice develops, as well as to predict temperature profile of pavement systems where a de-icing system is installed. In addition, the model can be used to determined the minimum energy required to melt the ice formed on the pavement. METHODS : The snow on the porous asphalt pavement, whose porosity must be considered in thermal analysis, is divided into several layers such as dry snow layer, saturated snow layer, water+pavement surface, pavement surface, and sublayer. The mass balance and heat balance equations are derived to describe conductive, convective, radiative, and latent transfer of heat and mass in each layer. The finite differential method is used to implement the derived equations, boundary conditions, and the testing method to determine the thermal properties are suggested for each layer. RESULTS: The finite differential equations that describe the icing and deicing on pavements are derived, and we have presented them in our work. The framework to develop a temperature-forecasting model is successfully created. CONCLUSIONS : We conclude by successfully creating framework for the finite difference model based on the heat and mass transfer theories. To complete implementation, laboratory tests required to be performed.

• 대한수학회지
• /
• 제58권3호
• /
• pp.553-569
• /
• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• 대한수학회보
• /
• 제52권5호
• /
• pp.1401-1422
• /
• 2015

Under the restriction of finite order, we prove two uniqueness theorems of nonconstant meromorphic functions sharing three values with their difference operators, which are counterparts of Theorem 2.1 in [6] for a finite-order meromorphic function and its shift operator.

• East Asian mathematical journal
• /
• 제24권4호
• /
• pp.407-414
• /
• 2008

Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations with damping and convection terms, which describe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1247-1256
• /
• 2009

Finite difference schemes are considered for a nonlinear $Ca^{2+}$ diffusion equations with stationary and mobile buffers. The scheme inherits mass conservation as for the classical solution. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained. using the extended Lax-Richtmyer equivalence theorem.

• Journal of Mechanical Science and Technology
• /
• 제19권11호
• /
• pp.2032-2039
• /
• 2005

The lattice Boltzman method (LBM) and the finite difference-based lattice Boltzmann method (FDLBM) are quite recent approaches for simulating fluid flow, which have been proven as valid and efficient tools in a variety of complex flow problems. They are considered attractive alternatives to conventional finite-difference schemes because they recover the Navier-Stokes equations and are computationally more stable, and easily parallelizable. However, most models of the LBM or FDLBM are for incompressible fluids because of the simplicity of the structure of the model. Although some models for compressible thermal fluids have been introduced, these models are for monatomic gases, and suffer from the instability in calculations. A lattice BGK model based on a finite difference scheme with an internal degree of freedom is employed and it is shown that a diatomic gas such as air is successfully simulated. In this research we present a 2-dimensional edge tone to predict the frequency characteristics of discrete oscillations of a jet-edge feedback cycle by the FDLBM in which any specific heat ratio $\gamma$ can be chosen freely. The jet is chosen long enough in order to guarantee the parabolic velocity profile of a jet at the outlet, and the edge is of an angle of $\alpha$=23$^{o}$. At a stand-off distance w, the edge is inserted along the centerline of the jet, and a sinuous instability wave with real frequency is assumed to be created in the vicinity of the nozzle exit and to propagate towards the downstream. We have succeeded in capturing very small pressure fluctuations resulting from periodic oscillation of the jet around the edge.