• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

• 한국항공우주학회지
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• 제35권7호
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• pp.586-591
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• 2007

예조건화 오일러 방정식의 수렴특성에 미치는 계산 오차의 영향을 해석하였다. 다양한 마하수의 원형 턱이 있는 이차원 관내 유동을 계산하였다. 마하수가 감소함에 따라 차분오차는 증가하는데, 에너지 방정식의 계산 오차는 다른 방정식의 계산 오차보다 빠르게 증가하는 것으로 나타났다. 그리고 예조건 행렬의 역행렬을 곱하여 변형된 지배방정식 형태를 이용하면 계산 오차 문제를 완화할 수 있음을 보였다

• 한국전자파학회논문지
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• 제25권10호
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• pp.1077-1086
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• 2014

컨포멀 배열에 적용할 수 있는 곡선 배열안테나용 Rotman 렌즈의 설계 방법을 제안한다. 본 논문에서는 곡선 배열안테나와 연동하여 Rotman 렌즈의 평행판 영역에 존재하는 배열 포트의 위치와, 배열 포트와 배열안테나 소자를 연결하는 전송선의 길이를 구하는 설계식을 유도하고, 이 설계식을 바탕으로 빔 곡선 최적화 절차와 재초점 절차를 통하여 위상 오차를 최소화하고 있다. 제안된 설계식과 설계 절차에 의해 설계된 Rotman 렌즈는 정확히 3초점을 보유한 채 직선 배열안테나뿐만 아니라, 원곡선, 포물선, V자형 곡선 등의 오목하거나 볼록한 배열안테나를 급전할 수 있으며, 최소의 위상 오차를 나타내고 있다.

• 충청수학회지
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• 제19권2호
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• pp.123-131
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• 2006

In this paper, a numerical programming for Liapunov index of differential equations with periodic coefficients depending on parameters is given. The associated equations are given at first, then existence of periodic solutions to the associated equations is proved in this paper. And we compute periodic solution u(t) of the associated equations. Finally, we give the error of approximate calculation.

• 호남수학학술지
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• 제27권2호
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• pp.317-332
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• 2005

In this paper we consider the hp-version to solve non-constant coefficients elliptic equations on a bounded, convex polygonal domain ${\Omega}$ in $R^2$. A family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties can be used for calculating the integrals. When the numerical quadrature rules $I_m{\in}G_p$ are used for computing the integrals in the stiffness matrix of the variational form we will give its variational form and derive an error estimate of ${\parallel}u-{\widetilde{u}}^h_p{\parallel}_{1,{\Omega}$.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.299-306
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• 2008

Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations, which discribe $Ca^{2+}$ 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.

• 대한수학회보
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• 제53권6호
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• pp.1725-1739
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• 2016

Abstract. Numerical solutions for the evolutionary space fractional order differential equations are considered. A predictor corrector method is applied in order to obtain numerical solutions for the equation without solving nonlinear systems iteratively at every time step. Theoretical error estimates are performed and computational results are given to show the theoretical results.

• Korean Journal of Mathematics
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• 제13권1호
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• pp.113-122
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• 2005

We consider the iterative schemes for the large sparse linear system to solve partial differential equations. Using spectral radius of iteration matrices, the optimal relaxation parameters and good parameters can be obtained. With those parameters we compare the effectiveness of the SOR and SSOR algorithms. Applying Crank-Nicolson approximation, we observe the error distribution according to domain decomposition. The number of processors due to domain decomposition affects time and error. Numerical experiments show that effectiveness of SOR and SSOR can be reversed as time size varies, which is not the usual case. Finally, these phenomena suggest conjectures about equilibrium time grid for SOR and SSOR.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.223-235
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• 2006

By applying the Landau-type transformation, we transform a Stefan problem with nonlinear free boundary condition into a system consisting of a parabolic equation and the ordinary differential equations. Fully discrete finite element method is developed to approximate the solution of a system of a parabolic equation and the ordinary differential equations. We derive optimal orders of convergence of fully discrete approximations in $L_2,\;H^1$ and $H^2$ normed spaces.

• 대한수학회지
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• 제34권3호
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• pp.515-531
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• 1997

In this paper, finite difference method is applied to approximate the generalized solutions of Sobolev equations. Using the Steklov mollifier and Bramble-Hilbert Lemma, a priori error estimates in discrete $L^2$ as well as in discrete $H^1$ norms are derived frist for the semidiscrete methods. For the fully discrete schemes, both backward Euler and Crank-Nicolson methods are discussed and related error analyses are also presented.