• 대한수학회논문집
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• 제38권1호
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• pp.281-298
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• 2023

A class of systems of Caputo fractional differential equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a uniform mesh is proposed. Supremum norm is used to derive an error estimate which is of order κ − 1, 1 < κ < 2. Numerical examples are given which validate our theoretical results.

• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.735-748
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• 1998

We analyze the error in the p version of the of the finite element method when the effect of the quadrature error is taken in the load vector. We briefly study some results on the $H^{1}$ norm error and present some new results for the error in the $L^{2}$ norm. We inves-tigate the quadrature error due to the numerical integration of the right hand side We present theoretical and computational examples showing the sharpness of our results.

• Nuclear Engineering and Technology
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• 제53권6호
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• pp.1878-1886
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• 2021

For industrial package (IP)-type transport containers for radioactive materials, a free drop test should be conducted under regulatory conditions. Owing to various uncertainties observed during the drop test, errors in drop angles inevitably occur. In IP-type metal transport containers in which the container directly impacts onto a rigid target without any shock absorbing materials, the error in the drop angle due to a slight misalignment makes a significant difference from the ideal drop. In particular, in a vertical drop, the error in the drop angle causes a strong secondary impact. In this paper, a numerical method is proposed to estimate the error in the drop angle occurring during the test. To determine this error, an optimization method accompanying a computational drop analysis is proposed, and a surrogate model is introduced to ensure calculation efficiency. Effectiveness of the proposed method is validated by performing the verification and comparison between the test and the analysis applied with the drop angle error.

• Structural Engineering and Mechanics
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• 제13권2호
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• pp.117-134
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• 2002

This paper presents a computational method for a confidence region of identified parameters which are affected by measurement noise and error contained in prescribed parameters. The method is based on sensitivities of the identified parameters with respect to model parameter error and measurement noise along with the law of error propagation. By conducting numerical experiments on simple models, it is confirmed that the confidence region coincides well with the results of numerical experiments. Furthermore, the optimum arrangement of sensor locations is evaluated when uncertainty exists in prescribed parameters, based on the concept that square sum of coefficients of variations of identified results attains minimum. Good agreement of the theoretical results with those of numerical simulation confirmed validity of the theory.

• 대한설비공학회:학술대회논문집
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• 대한설비공학회 2006년도 하계학술발표대회 논문집
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• pp.116-121
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• 2006

Numerical simulations for dendritic growth of crystals are conducted in this study by the level set method. The effect of order of difference is tested for reinitialization error in simple problems and authors founded in case of 1st order of difference that very fine grids have to be used to minimize the error and higher order of difference is desirable to minimize the reinitialization error The 2nd and 4th order Runge-Kutta scheme in time and 3rd and 5th order of WENO schemes with Godunov scheme are applied for space discretization. Numerical results are compared with the analytical theory, phase-field method and other researcher's level set method.

• 대한수학회보
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• 제39권1호
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• pp.9-22
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• 2002

We consider the hp-version to solve non-constant coefficient elliptic equations with Dirichlet boundary conditions on a bounded, convex polygonal domain $\Omega$ in $R^{2}.$ To compute the integrals in the variational formulation of the discrete problem we need the numerical quadrature rule scheme. In this paler we consider a family $G_{p}= {I_{m}}$ of numerical quadrature rules satisfying certain properties. When the numerical quadrature rules $I_{m}{\in}G_{p}$ are used for calculating the integrals in the stiffness matrix of the variational form we will give its variational fore and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_0,{\Omega}'$.

• 대한수학회보
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• 제47권6호
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• East Asian mathematical journal
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• 제14권1호
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• pp.63-76
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• 1998

we consider the hp-version to solve non-constant coefficients elliptic equations $-div(a{\nabla}u)=f$ with Dirichlet boundary conditions on a bounded polygonal domain $\Omega$ in $R^2$. In [6], M. Suri obtained an optimal error-estimate for the hp-version: ${\parallel}u-u^h_p{\parallel}_{1,\Omega}{\leq}Cp^{(\sigma-1)}h^{min(p,\sigma-1)}{\parallel}u{\parallel}_{\sigma,\Omega}$. This optimal result follows under the assumption that all integrations are performed exactly. In practice, the integrals are seldom computed exactly. The numerical quadrature rule scheme is needed to compute the integrals in the variational formulation of the discrete problem. In this paper we consider a family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties, which can be used for calculating the integrals. Under the numerical quadrature rules we will give the variational form of our non-constant coefficients elliptic problem and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_{1,\Omega}$.

• 전기학회논문지P
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• 제59권2호
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• pp.222-231
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• 2010

This paper presents numerical analysis of measurement errors of ground electrode using the fall-of-potential method. In order to analyze ground resistance error according to the positions of auxiliary probes, firstly, national and international standards were researched. Secondly, numerical ground resistance error of hemispheric electrode was analyzed according to the locations of auxiliary probes and the angle between probes. Then, error-reduced positions of auxiliary probes were shown according to the distance to auxiliary current probe versus ground electrode size. Finally, error compensation method was presented. The results presented in this paper provide useful information regarding ground resistance error of alternative positions of auxiliary probes in case that the auxiliary probes could not be located at the proper position in such cases as there are buildings, roadblock or underground metallic pipe at that position.

• 한국음향학회지
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• 제22권6호
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• pp.496-504
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• 2003

본 논문에서는 유전자 알고리즘을 이용하여 빔 패턴 오차의 허용범위를 만족하는 개별소자의 허용오차를 분석하였다. 기존의 수치적 통계방법은 배열소자의 개수증가에 따라 계산량이 증가하는 문제점이 있고 이를 보완하기 위해 제안된 Monte-Carlo 방법은 낮은 정밀도와 빔 패턴 합성으로의 확장이 어렵다는 한계점을 가지고 있어 본 논문에서는 이러한 단점을 극복하기 위해 유전자 알고리즘을 이용한 소나 배열 소자의 허용오차 분석법을 제안하였다. 제안된 알고리즘을 이용하여 1차원과 2차원 배열에서 주어진 빔 패턴 오차 허용범위를 만족하는 각 소자별 허용오차 범위를 분석하였고 모의실험을 통하여 소나 배열 소자의 허용오차 범위가 타당함을 검증하였다.