• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.963-982
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• 2013

The Galerkin method has been developed mainly for 2nd order differential equations. To get numerical solutions, there are some choices of Riesz bases for the approximation subspace $V_j{\subset}L^2$. In this paper we shall propose a uniform approach to find suitable Riesz bases for higher order differential equations. Especially for the beam equation (4-th order equation), we also report numerical results.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.76.1-76
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• 2002

This paper addresses a method for nonlinear controller construction for a general nonlinear system with the separation of controller construction and manipulated values generation. The nonlinear system model is firstly expressed with the coefficients of state-depended representation. The nonlinear control is designed without any approximation based on the model with state-depended representation. At the stage of controller implementation for the nonlinear system, the manipulated values are calculated accurately by use of an algorithm of the numerical analysis. The numerical error for calculating the manipulated value can be reduced to zero by selecting the sampling interval being a small val...

• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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• pp.215-220
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• 2008

A numerical method for gas-liquid two-phase flow is applied to solve shock-bubble interaction problems. The present method employs a finite-difference Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL-TVD scheme. A homogeneous equilibrium cavitation model is used. By this method, a Riemann problem for shock tube was computed for validation. Then, shock-bubble interaction problems between cylindrical bubbles located in the liquid and incident liquid shock wave are computed.

• 한국전산유체공학회:학술대회논문집
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• 2008.10a
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• pp.215-220
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• 2008

A numerical method for gas-liquid two-phase flow is applied to solve shock-bubble interaction problems. The present method employs a finite-difference Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL-TVD scheme. A homogeneous equilibrium cavitation model is used. By this method, a Riemann problem for shock tube was computed for validation. Then, shock-bubble interaction problems between cylindrical bubbles located in the liquid and incident liquid shock wave are computed.

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.1155-1158
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• 1999

In this paper, we consider the optimal control of detection threshold to minimize the conditional mean-square state estimation error for the probabilistic data association (PDA) filter. Earlier works on this problem involved the cumbersome graphical optimization algorithm or time-consuming numerical optimization algorithm. Using the numerical approximation of information reduction factor, we obtained the closed-form optimal detection threshold. This results are very useful for real-time implemenation.

• 한국전산유체공학회:학술대회논문집
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• 2008.03b
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• pp.358-361
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• 2008

A study is made of thermal plume flow model for the development of helicopter simulator over the forest fire. For numerical analysis, the Boussinesq fluid approximation and line fire model, which is assumed by the shape of forest fire spreading, are adopted. Comparing 3-D full numerical solutions with 2-D similarity solution, it has been built a new model that is capable of temperature prediction along the symmetric vertical axis in both cases of laminar and turbulent flows.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.99-112
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• 2012

This paper attempts to present a numerical method for solving optimal control problems. The method is based upon constructing the n-th degree Jacobi polynomials to approximate the control vector and use differentiation matrix to approximate derivative term in the state system. The system dynamics are then converted into system of algebraic equations and hence the optimal control problem is reduced to constrained optimization problem. Numerical examples illustrate the robustness, accuracy and efficiency of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.8
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• pp.1434-1439
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• 2008

Numerical methods for solving the state feedback control problem of linear time invariant system are presented in this paper. The methods are based on Haar wavelet approximation. The properties of Haar wavelet are first presented. The operational matrix of integration and its inverse matrix are then utilized to reduce the state feedback control problem to the solution of algebraic matrix equations. The proposed methods reduce the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity and applicability of the proposed methods.

• The Mathematical Education
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• v.37 no.1
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• pp.101-114
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• 1998

In this thesis, We tried to introduce definite integration to the curriculum of high school mathematics with numerical integration, which had been introduced with quadrature method. For this purpose, We used new experimental mathematics approaches, so-called investigation and examination. In chapter II, We examined how much computers had been used in teaching mathematics. In chapter III, We presented the theoretical background of approximation integration within numerical integration. In chapter IV, We studied and compared various methods of numerical integration, and examined the relation between curvature of a curved line and numerical integration. In order to study more easily, We used some of computer programs. We hope that this thesis will be a turning point in developing new teaching methods and improving curriculum of mathematics in high school.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.6
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• pp.1034-1043
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• 2015

This is the continuation of a numerical study on vortex shedding from a blunt trailing-edge of a hydrofoil. In our previous work (Lee et al., 2015), numerical schemes for efficient computations were successfully implemented; i.e. multiple domains, the approximation of domain boundary conditions using cubic spline functions, and particle-based domain decomposition for better load balancing. In this study, numerical results through a hybrid particle-mesh method which adopts the Vortex-In-Cell (VIC) method and the Brinkman penalization model are further rigorously validated through comparison to experimental data at the Reynolds number of $2{\times}10^6$. The effects of changes in numerical parameters are also explored herein. We find that the present numerical method enables us to reasonably simulate vortex shedding phenomenon, as well as turbulent wakes of a hydrofoil.