• Kyungpook Mathematical Journal
• /
• 제47권4호
• /
• pp.529-548
• /
• 2007

The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

• 대한수학회지
• /
• 제59권5호
• /
• pp.891-909
• /
• 2022

The main objective of this paper is to develop a concrete inverse formula of the system induced by the fourth-order finite difference method for two-point boundary value problems with Robin boundary conditions. This inverse formula facilitates to make a fast algorithm for solving the problems. Our numerical results show the efficiency and accuracy of the proposed method, which is implemented by the Thomas algorithm.

• 전기전자학회논문지
• /
• 제23권3호
• /
• pp.817-825
• /
• 2019

마이크로프로세서를 이용한 제어알고리즘 구현에서 차분방정식이 매우 유용하게 사용된다. 샘플링 데이터로부터 미분 값을 추정하기 위해 전향, 후향 및 중심 차분 방식이 사용되어왔다. 차분 값을 계산하기 위해서는 차분계수가 매우 중요하다. 본 논문에서는 유한 차분 계수를 계산하기 위한 새로운 방식을 제시하고자 한다. 제안된 방식의 유효성을 입증하기 위해 RLS 알고리즘을 적용한 파라미터 추정에 대하여 적용하였다.

• 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.

• Journal of electromagnetic engineering and science
• /
• 제9권1호
• /
• pp.12-16
• /
• 2009

This paper presents a new iterative locally one-dimensional [mite-difference time-domain(LOD-FDTD) method that has a simpler formula than the original iterative LOD-FDTD formula[l]. There are fewer arithmetic operations than in the original LOD-FDTD scheme. This leads to a reduction of CPU time compared to the original LOD-FDTD method while the new method exhibits the same numerical accuracy as the iterative ADI-FDTD scheme. The number of arithmetic operations shows that the efficiency of this method has been improved approximately 20 % over the original iterative LOD-FDTD method.

• 대한조선학회지
• /
• 제19권4호
• /
• pp.19-29
• /
• 1982

Galerkin's finite element method is applied to a two-dimensional heat convection-diffusion problem arising in the hydrodynamic lubrication of thrust bearings used in naval vessels. A parabolized thermal energy equation for the lubricant, and thermal diffusion equations for both bearing pad and the collar are treated together, with proper juncture conditions on the interface boundaries. it has been known that a numerical instability arises when the classical Galerkin's method, which is equivalent to a centered difference approximation, is applied to a parabolic-type partial differential equation. Probably the simplest remedy for this instability is to use a one-sided finite difference formula for the first derivative term in the finite difference method. However, in the present coupled heat convection-diffusion problem in which the governing equation is parabolized in a subdomain(Lubricant), uniformly stable numerical solutions for a wide range of the Peclet number are obtained in the numerical test based on Galerkin's classical finite element method. In the present numerical convergence errors in several error norms are presented in the first model problem. Additional numerical results for a more realistic bearing lubrication problem are presented for a second numerical model.

• Tribology and Lubricants
• /
• 제12권3호
• /
• pp.115-122
• /
• 1996

In this paper, a finite difference method and the Newton-Raphson method are used to evaluate the Hamrock and Dowson's EHL film thickness formulas in elliptical contact problems. The minimum and central film thicknesses are compared with the Hamrock and Dowson's numerical results for various dimensionless parameters and with their film thickness formulas. The results of present analysis are more accurate and physically reasonable. The minimum film thickness formula is similar with the Hamrock and Dowson's results, however, the central film thickness formula shows large differences. Therefore, the Hamrock and Dowson's central film thickness formula should be replaced by following equation. $H_{c} = 4.88U^{0.68}G^{0.44}W^{0.096}(1-0.58e^{-0.60k})$ More accurate film thickness formula for general elliptical contact problems can be expected using present numerical methods and further research should be required.

• Journal of applied mathematics & informatics
• /
• 제8권2호
• /
• pp.473-489
• /
• 2001

The notion of difference for two convex compact sets in Rⁿ, proposed by Rubinov et al, is generalized to R/sub mxn/. A formula of the difference for the two sets, which are convex hulls of a finite number of points, is developed. In the light of this difference, the relation between Clarke generalized Jacobian and quasidifferential, in the sense of Demyanov and Rubinov, for a nonsnooth function, is established. Based on the relation, the method of estimating Clarke generalized Jacobian via quasidifferential for a certain class of function, is presented.

• Communications for Statistical Applications and Methods
• /
• 제23권1호
• /
• pp.21-32
• /
• 2016

We study asymptotic expansion formulae for numerical computation of Greeks (i.e. sensitivity) in finance. Our approach is based on the integration-by-parts formula of the Malliavin calculus. We propose asymptotic expansion of Greeks for a stochastic volatility model using the Greeks formula of the Black-Scholes model. A singular perturbation method is applied to derive asymptotic Greeks formulae. We also provide numerical simulation of our method and compare it to the Monte Carlo finite difference approach.

• 한국지반환경공학회 논문집
• /
• 제12권11호
• /
• pp.23-30
• /
• 2011

본 연구에서는 터널의 상부에 작용하는 토압을 평가하는데 있어서 기존의 Terzaghi 공식이 가지는 문제점을 해결하기 위해 흙의 팽창성(Dilatancy)을 고려하여 Terzaghi 공식을 수정하였다. Terzaghi 공식과 수정식에 대한 수학적 해석결과, 터널의 토압은 수정식이 Terzaghi 공식에 비해 작게 나타났으며 토피고가 커질수록 그 차이는 증가하였다. 터널모형실험 결과와 비교해 본 결과, Terzaghi 공식에 의해 계산된 상부토압은 굴착 전 토압의 약 70%이며, 수정식에 의하면 약 60% 정도로 나타났고, 터널모형실험에 의해 측정된 토압은 약 40% 정도 임을 볼 수 있었다. 또한 유한요소해석을 이용하여 Terzaghi 공식과 수정식에 의해 산정된 터널 상부토압과 전단변형률을 비교해본 결과 수학적 해석결과와 동일하게 수정식이 Terzaghi 공식보다 작게 나타났다.