• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.319-328
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• 2004

In this paper we investigate the qualitative behaviour of numerical approximation to a class delay differential equation. We consider the numerical solution of the delay differential equations undergoing a Hopf bifurcation. We prove the numerical approximation of delay differential equation had a Hopf bifurcation point if the true solution does.

• 대한수학회논문집
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• 제15권1호
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• pp.133-142
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• 2000

We consider some numerical solution methods for equilibrium equations Af + E$^{T}$ λ = r, Ef = s. Algebraic problems of this form evolve from many applications such as structural optimization, fluid flow, and circuits. An important approach, called the force method, to the solution to such problems involves dimension reduction nullspace computation for E. The purpose of this paper is to investigate the substructuring method for the solution step of the force method in the context of the incompressible fluid flow. We also suggests some iterative methods based upon substructuring scheme..

• Korean Journal of Mathematics
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• 제13권2호
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• pp.161-176
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• 2005

We consider a model of population dynamics whose mortality function is unbounded. We note that the regularity of the solution depends on the growth rate of the mortality near the maximum age. We propose Gauss-Legendre methods along the characteristics to approximate the solution when the solution is smooth enough. It is proven that the scheme is convergent at fourth-order rate in the maximum norm. We also propose discontinuous Galerkin finite element methods to approximate the solution which is not smooth enough. The stability of the method is discussed. Several numerical examples are presented.

• 대한기계학회논문집B
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• 제32권9호
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• pp.676-682
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• 2008

Numerical analysis was carried out to examine the heat transfer and pressure drop characteristics of plate heat exchangers for absorption application using Computational Fluid Dynamics(CFD) technique. A commercial CFD software package, FLUENT was used to predict the characteristics of heat transfer, pressure drop and flow distribution within plate heat exchangers. In this paper, a welded plate heat exchanger with the plate of chevron embossing type was numerically analyzed by controlling mass flow rate, solution concentration, and inlet temperatures. The working fluid is $H_2O$/LiBr solution with the LiBr concentration of 50-60% in mass. The numerical simulation shows reasonably good agreement with the experimental results. Also, the numerical results show that plate of the chevron shape gives better results than plate of the elliptical shape from the view points of heat transfer and pressure drop. These results provide a guideline to apply the welded PHE for the solution heat exchanger of absorption systems.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.675-694
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• 2022

In this article, we investigate the solution of the inverse problem for one dimensional heat equation with Neumann and Robin boundary conditions, that is, we determine the temperature and source term with given initial and boundary conditions. Three radial basis functions(RBFs) have been used for numerical solution, and Homotopy perturbation method for analytic solution. Numerical solutions which are obtained by considering each of the three RBFs are compared to the exact solution. For appropriate value of shape parameter c, numerical solutions best approximates exact solutions. Furthermore, we have shown the impact of noisy data on the numerical solution of u and f.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권4호
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• pp.201-210
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• 2010

We propose a new robust and accurate method for the numerical solution of medical image segmentation. The modified Allen-Cahn equation is used to model the boundaries of the image regions. Its numerical algorithm is based on operator splitting techniques. In the first step of the splitting scheme, we implicitly solve the heat equation with the variable diffusive coefficient and a source term. Then, in the second step, using a closed-form solution for the nonlinear equation, we get an analytic solution. We overcome the time step constraint associated with most numerical implementations of geometric active contours. We demonstrate performance of the proposed image segmentation algorithm on several artificial as well as real image examples.

• 대한수학회보
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• 제55권3호
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• pp.881-898
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• 2018

This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible Navier-Stokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudo-time derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.

• Coupled systems mechanics
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• 제2권3호
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• pp.271-288
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• 2013

In the present study an elastic-plastic strain analysis is carried out for fibrous composites by using numerical modeling. Application of homogeneous transversely-isotropic model was chosen based on problem solution of a square plate with a circular hole under uniaxial tension. The results obtained in this study correspond to the solution of fiber model trial problem, as well as to analytical solution. Further, numerical algorithm and software has been developed, based on simplified theory of small elastic strains for transversely-isotropic bodies, and FEM. The influence of holes and cracks on stress state of complicated configuration transversely-isotropic bodies has been studied. Strain curves and plasticity zones that are formed in vicinity of the concentrators has been provided. Numerical values of effective mechanical parameters calculated for unidirectional composites at different ratios of fiber volume content and matrix. Content volume proportions of fibers and matrix defined for fibrous composite material that enables to behave as elastic-plastic body or as a brittle material. The influences of the fibrous structure on stress concentration in vicinity of holes on boron/aluminum D16, used as an example.

• East Asian mathematical journal
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• 제33권5호
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• pp.495-509
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• 2017

With the accuracy of the nonlinearity guaranteed, plenty of time and large memory space are needed when we solve the finite element numerical solution of nonlinear partial differential equations. In this paper, we use the Group Element Method (GEM) to deal with the non-linearity of the BBM-Burgers Equation with Conservation form and perform a numerical analysis for two particular initial-boundary value (the Dirichlet boundary conditions and Neumann-Dirichlet boundary conditions) problems with the Finite Element Method (FEM). Some numerical experiments are performed to analyze the error between the exact solution and the FEM solution in MATLAB.

• 대한기계학회논문집A
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• 제22권3호
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• pp.519-528
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• 1998

A numerical method is presented for the dynamic analysis of cam and follower. Contact and separation between the cam and the follower are analyzed by imposing dynamic contact condition. The correct solution is obtained without spurious oscillation by imposing the velocity and acceleration constraints as well as the displacement constraint on the possible contact point. The constraints are satisfied by iteratively reducing the constraint errors toward zero, and a simple time integration of ordinary differential equation is employed for the solution of the equation of motion. The solution procedure associated with the iterative scheme is presented, and numerical simulations are conducted to demonstrate the accuracy of the solution.