• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.699-713
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• 2022

This paper proposes a hybrid successive over-relaxation iterative method for the numerical solution of a nonlinear diffusion in a one-dimensional porous medium. The considered mathematical model is discretized using a computational complexity reduction scheme called half-sweep finite differences. The local truncation error and the analysis of the stability of the scheme are discussed. The proposed iterative method, which uses explicit group technique and modified successive over-relaxation, is formulated systematically. This method improves the efficiency of obtaining the solution in terms of total iterations and program elapsed time. The accuracy of the proposed method, which is measured using the magnitude of absolute errors, is promising. Numerical convergence tests of the proposed method are also provided. Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods.

• Structural Engineering and Mechanics
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• 제61권5호
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• pp.657-661
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• 2017

In this paper, it has been tried to propose a new semi analytical approach for solving nonlinear vibration of conservative systems. Hamiltonian approach is presented and applied to high nonlinear vibration systems. Hamiltonian approach leads us to high accurate solution using only one iteration. The method doesn't need any small perturbation and sufficiently accurate to both linear and nonlinear problems in engineering. The results are compared with numerical solution using Runge-Kutta-algorithm. The procedure of numerical solution are presented in detail. Hamiltonian approach could be simply apply to other powerfully non-natural oscillations and it could be found widely feasible in engineering and science.

• Structural Engineering and Mechanics
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• 제69권5호
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• pp.479-486
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• 2019

Based on the displacement general solution of a pre-twisted Euler-Bernoulli beam, the shape function and stiffness matrix are deduced, and a new finite element model is proposed. Comparison analyses are made between the new proposed numerical model based on displacement general solution and the ANSYS solution by Beam188 element based on infinite approach. The results show that developed numerical model is available for the pre-twisted Euler-Bernoulli beam, and that also provide an accuracy finite element model for the numerical analysis. The effects of pre-twisted angle and flexural stiffness ratio on the mechanical property are also investigated.

• 한국항만학회지
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• 제5권1호
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• pp.71-81
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• 1991

This study deals with the analytical and numerical solution for the combined wave reflection and diffraction near the impermeable rigid upright breakwater, subject to the excitation of a plane simple harmonic wave coming from infinity. Three cases are presented : a) the analytical solution near a thin semi-infinite breakwater, b) the analytical solution near the semi-infinite breakwaters of arbitrary edge angles, $30^{\circ},\;45^{\circ},\;and\;90^{\circ}$, c) the numerical solution near a detached thin breakwater the results are presented in amplification factor and wave height diagrams. Moreover, the amplification factors near the structure(2 wavelength before and behind the structure) are compared for the given cases. A finite difference technique for the numerical solution was applied to the integral equation obtained for the wave potential.

• 한국방재학회 논문집
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• 제8권1호
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• pp.133-138
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• 2008

외해에서 내습하는 파랑 자료를 분석하는 일은 연안에서 발생하는 문제를 해결함에 있어 기본이 되기 때문에 매우 중요하다. 파랑을 해석하는 방법에는 크게 수치 모델을 이용하는 방법과 해석 해를 이용하는 방법이 있다. 수치 모델의 경우, 다양한 지형과 파랑 조건에 대해 적용할 수 있다는 장점이 있지만 수치 오차를 고려해야 하는 번거로움이 있다. 반면, 해석 해의 경우 수치 오차 없이 빠르고 정확하게 해를 구할 수 있다는 장점이 있지만 특정한 지형 및 파랑 조건에서만 성립한다는 단점이 있다. 본 연구에서는 수치적인 기법과 해석적인 접근을 혼합하여 수치 오차를 최소화시키면서 다양한 조건에 적용이 가능한 완경사 방정식의 해를 유도하였다. 유도된 해를 기존의 수치 해와 비교한 결과 매우 잘 일치한다는 알 수 있었다.

• 에너지공학
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• 제19권3호
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• pp.143-150
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• 2010

선형열원 해석은 열원 주위가 완전히 균일한 매질로 이루어져 있다는 가정 하에 성립되는 해석이나 실제 보어홀 시스템의 경우 그라우팅 영역은 주위토양과 매우 다른 열물성치를 가진 물질로 이루어져 있다. 본 연구에서는 이러한 그라우팅 영역이 선형열원 해석에 어떠한 영향을 미치는가를 연구하였다. 연구방법으로는 먼저 수치모델을 개발하고 이 수치모델에 의하여 시간에 따른 보어홀 유체온도를 생성한 후 이 유체온도를 선형열원법에 이용하여 지중열전도도와 보어홀 전열저항을 구하며 이렇게 구한 해를 수치모델의 입력조건과 비교함으로서 그 차이점을 규명한다. 이러한 해석결과 선형열원법의 해인 지중열전도도와 보어홀 전열 저항은 수치모델 입력조건에 비해 대략, 86%와 91%의 수준으로 나타났다. 선형열원 해로부터 수치모델의 입력조건을 역산해 나가는 Chart법이 본 연구에서 개발되었으며 시험용 보어홀의 열응답시험 결과와 비교해 본 결과 이 Chart법은 신뢰성이 있는 것으로 나타났다. 그라우트 영역의 열물성치를 변화시켜가며 선형열원해의 특성이 어떻게 변하는지도 검토하였다.

• Journal of Advanced Marine Engineering and Technology
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• 제30권5호
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• pp.597-607
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• 2006

This paper presents a numerical simulation of the behavior of the LiBr solution droplets and falling films in horizontal tube banks of absorber. The model developed here accounts for the details of the droplets formation and impact process for absorption on horizontal tubes including the heat transfer from solution film to the tube wall. Especially. the characteristic of unsteady behavior of solution flow has been investigated. Flow visualization studies shown that the solution droplets and falling films have some of the complex characteristics. It is found that. with the numerical conditions similar to the operating condition of an actual absorption chiller/heater, the outlet solution temperature and heat flux from solution film to the tube wall have a stable periodic behavior with time. The solution droplets and falling films in horizontal tube banks of absorber is a periodic unsteady flow. The results from this model are compared with previous experimental observation taken with a high-speed digital video camera and shown good agreement.

• Journal of applied mathematics & informatics
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• 제8권1호
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• pp.45-57
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• 2001

A parametric scheme is proposed for the numerical solution of the nonlinear Boussinesq equation. The numerical method is developed by approximating the time and the space partical derivatives by finite-difference re placements and the nonlinear term by an appropriate linearized scheme. The resulting finite-difference method is analyzed for local truncation error and stability. The results of a number of numerical experiments are given for both the single and the double-soliton wave. AMS Mathematics Subject Classification : 65J15, 47H17, 49D15.

• 대한수학회논문집
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• 제11권3호
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• pp.867-880
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• 1996

Numerical approximations to the linear elasticity are traditionally based on the finite element method. In this paper we propose a new formulation based on the cubic spline collocation method for linear elastic problem on the unit square. We present several numerical results for the eigenvalues of the matrix represented by cubic collocation method and preconditioner matrix which is preconditioned by FEM and FDM. Finally we present the numerical solution for some example equation.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.113-124
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• 2006

In this paper we consider the numerical solution of the sunflower equation. We prove that if the sunflower equation has a Hopf bifurcation point at a = ao, then the numerical solution with the Euler-method of the equation has a Hopf bifurcation point at ah = ao + O(h).