• Korean Journal of Mathematics
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• 제13권2호
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• pp.149-159
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• 2005

We study an age-dependent s-i-s epidemic model with spatial diffusion. The model equations are described by a nonlinear and nonlocal system of integro-differential equations. Finite difference methods along the characteristics in age-time domain combined with finite elements in the spatial variable are applied to approximate the solution of the model. Stability of the discrete periodic solution is investigated.

• Elastomers and Composites
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• 제38권2호
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• pp.175-179
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• 2003

For the total description of mechanical behaviors of elastomers, it is necessary to know the so-called rheological constitutive equation i.e. the strain-energy density function (W) in case of elastomers, which necessitates biaxial tensile results of elastic body. This paper first describes the experimental results of biaxial tensile measurements on poly(siloxane) model networks. W was estimated from its differential form i.e. the $1^{st}$ differential of W is stress. The W was found to reproduce the experimental stress-strain results, and the W estimated for silica filled poly(siloxane) networks suggest a different behavior between conventional precipitated silica and in situ formed silica. The difference suggests the different surface property of the two silicas.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.373-378
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• 1998

A method to construct a memoryless feedback law for systems with multiple time-delays in the states is proposed. As a plant model, a differential-difference equation with multiple delayed terms is introduced, A stabilizability condition by memoryless feedback is presented. A feedback gain is calculated with a solution of a finite dimensional Riccati equation. It is shown that the resulting closed loop system is asymptotically stable, and moreover, it is a linear quadratic regulator for some cost functional. An alternative stabilizability condition which is easier to check is given.

• 산업기술연구
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• 제14권
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• pp.19-28
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• 1994

일반적으로 2차원 Poisson 방정식을 풀기 위해 유한 차분법을 이용하여 tridiagonal block Toeplitz 선형방정식을 얻는다. 이 선형방정식의 독특한 형태를 활용하기 위해 Lyapunov 방정식으로 변화시킨 다음 이산정현변환(DST)을 이용해서 대각선 행렬로 만들면 계산이 용이해진다. 또 DST는 FFT를 이용해 계산할 수 있으므로 고속 계산이 가능하다. FFT를 병렬로 처리하기 위해 프로세서가 4,096개인 SIMD 컴퓨터 MP-2에서 시뮬레이션했다. 본 논문에서는 알고리즘 유도, 매핑 및 시뮬레이션 결과를 제시했다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권3호
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

• Journal of applied mathematics & informatics
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• 제8권3호
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• pp.743-753
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• 2001

We provide local convergence results in affine form for inexact Newton-like as well as quasi-Newton iterative methods in a Banach space setting. We use hypotheses on the second or on the first and mth Frechet-derivative (m≥2 an integer) of the operator involved. Our results allow a wider choice of starting points since our radius of convergence can be larger than the corresponding one given in earlier results using hypotheses on the first-Frechet-derivative only. A numerical example is provided to illustrate this fact. Our results apply when the method is, for example, a difference Newton-like or update-Newton method. Furthermore, our results have direct applications to the solution of autonomous differential equations.

• 한국공작기계학회논문집
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• 제10권1호
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• pp.112-119
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• 2001

Design sensitivity is an important is an important device in improving a mechanical system design. A continuum design consists of the shape and orientation design. This research develops the shape and orientation design sensitivity method. The configura-tion design variables of multibody systems define the shape and orientation changes. The equations of motion are directly differentiated to obtain the governing equations for the design sensitivity. The governing equation of the design sensitivity is formulated as an over determined differential algebraic equation and treated as ordinary differential equations on mani-folds. The material derivative of a domain functional is performed to obtain the sensitivity due to shape and orientation changes. The configuration design sensitivities of a fly-ball governor system and a spatial four bar mechanism are obtained using the proposed method and are validated against those obtained from the finite difference method.

• 대한조선학회지
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• 제13권1호
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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.

• 한국전산구조공학회논문집
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• 제29권3호
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• pp.237-244
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• 2016

본 연구는 재료비선형 문제를 다루기 위한 비선형 MLS 차분법의 정식화 과정을 제시한다. MLS 차분법은 절점모델을 기반으로 고속 미분근사식을 활용하여 지배 미분방정식을 직접 이산화 하는데, 변수를 변위로 일원화한 Navier 방정식을 사용하여 탄성재료 문제를 다룬 기존의 MLS 차분법은 재료의 구성방정식을 별도로 고려할 수 없다. 본 연구에서는 비선형 재료의 구성방정식을 반영할 수 있는 강정식화를 위해 1차 미분근사를 반복 사용하는 겹미분근사를 고안했다. 응력의 발산으로 표현되는 평형방정식을 그대로 이산화하고 Newton 방법을 적용하여 반복계산을 통해 수렴해를 찾는 비선형 알고리즘을 제시했다. 응력 계산과 내부변수의 갱신은 return mapping 알고리즘을 활용하였고, 알고리즘 접선계수(algorithmic tangent modulus)의 적용을 통해 빠르고 안정적인 반복계산이 가능하도록 하였다. 재생성 시험을 통해 겹미분근사의 정당성을 검증했고, 비선형재료에 대한 인장문제의 해석을 통해 개발된 비선형 MLS 차분 알고리즘의 정확성과 안정성을 확인하였다.

• 충청수학회지
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• 제29권3호
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• pp.503-508
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• 2016

We propose a number of finite difference methods for the prices of a European option under the CGMY model. These numerical methods to solve a partial integro-differential equation (PIDE) are based on three time levels in order to avoid fixed point iterations arising from an integral operator. Numerical simulations are carried out to compare these methods with each other for pricing the European option under the CGMY model.