• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.615-632
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• 1998

Soliton solutions of a class of generalized nonlinear evo-lution equations are discussed analytically and numerically which is achieved using a travelling wave method to formulate one-soliton solution and the finite difference method to the numerical dolutions and the interactions between the solitons for the generalized nonlinear Schrodinger equations. The characteristic behavior of the nonlinear-ity admitted in the system has been investigated and the soliton state of the system in the limit of $\alpha\;\longrightarrow\;0$ and $\alpha\;\longrightarrow\;\infty$ has been studied. The results presented show that soliton phenomena are character-istics associated with the nonlinearities of the dynamical systems.

• Journal of Advanced Marine Engineering and Technology
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• 제31권8호
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• pp.954-960
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• 2007

The purpose of this paper is to obtain design method of air-distribution system. Air-distribution system is composed of blower, duct, diffusers and measuring equipment. The air-flow rate from each diffuser is not equal. The air-flow rate is calculated with the combined equations which are Bernoulli's equation, continuity equation and minor loss equations. Inlet condition and outlet condition are adapted in each duct system. Then square difference between function of maximum air-flow rate and minimum air-flow rate is used as an object function. Area of diffuser and velocity are established as constraints. To minimize the object function, the optimization method is used. After optimization the design variables are selected under satisfaction of constraints. The air-distribution system is calculated again with the result of optimized design variable. It is shown that the air-distribution system has the equal air-flow rate from diffusers.

• 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.

• 대한수학회보
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• 제61권1호
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• pp.93-115
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• 2024

In this paper, the Gauge-Uzawa methods for the Darcy-Brinkman equations driven by temperature and salt concentration (DBTC) are proposed. The first order backward difference formula is adopted to approximate the time derivative term, and the linear term is treated implicitly, the nonlinear terms are treated semi-implicit. In each time step, the coupling elliptic problems of velocity, temperature and salt concentration are solved, and then the pressure is solved. The unconditional stability and error estimations of the first order semi-discrete scheme are derived, at the same time, the unconditional stability of the first order fully discrete scheme is obtained. Some numerical experiments verify the theoretical prediction and show the effectiveness of the proposed methods.

• 대한전기학회논문지
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• 제33권3호
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• pp.91-99
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• 1984

Time-optimal control for dmping a one-dimensional xenon-induced spatial power oscillations in pressurized water reactor is studied. Linearized system equations describing the spatial xenon oscillations have been derived based on lambda mode analysis. Optimal control strategies, eventually bang-bang controls, have been drawn applying Pontryagins Minimum Principle, subject to a band constraint on available contros strength. Validity of the linearized system equations and optimal control strategies derived has been demonstrated through conputer simulations which incorporate the finite difference method for one dimensional axial geometry, for the soulution of the two-group neutron diffusion equations. The results obtained through computer simulations show that xenon-induced transients can be suppressed successfully with bang-bang control.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.665-732
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• 2015

Existence results for multiple positive solutions of two classes of boundary value problems for bilateral difference systems are established by using a fixed point theorem under convenient assumptions. It is the purpose of this paper to show that the approach to get positive solutions of boundary value problems of finite difference equations by using multi-fixed-point theorems can be extended to treat the bilateral difference systems with one-dimensional Laplacians. As an application, the sufficient conditions are established for finding multiple positive homoclinic solutions of a bilateral difference system. The methods used in this paper may be useful for numerical simulation. An example is presented to illustrate the main theorems. Further studies are proposed at the end of the paper.

• 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.

• 대한기계학회논문집
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• 제15권6호
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• pp.1861-1871
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• 1991

본 연구에서는 아직까지 연구가 미진한 내용 즉, 유속과 압력이 시간과 위치 의 함수인 유동특성과 파이프의 운동이 상호 연계되어 영향을 주는 일반적인 경우의 운동방정식을 유도하였고 단순지지된 직선 파이프를 모델로 설정하여 동적 안정성 (dynamic stability)과 진동응답을 수치적으로 고찰하였다.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.19-35
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• 2004

We develop in this paper some preconditioners for sparse non-symmetric M-matrices, which combine a recursive two-level block I LU factorization with multigrid method, we compare these preconditioners on matrices arising from discretized convection-diffusion equations using up-wind finite difference schemes and multigrid orderings, some comparison theorems and experiment results are demonstrated.