• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.935-942
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• 2001

A finite element approximation of a fourth-order nonlinear boundary value problem is given. In the direct implementation, a nonlinear system will be obtained and also a full size matrix will be introduced when Newton’s method is adopted to solve the system. To avoid this difficulty we introduce an iterative scheme which can be shown to converge the positive solution of the system lying between 0 and $sin{\pi}x$.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1109-1118
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• 2009

In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, $\{({\phi}_p(x'(t)))'+h(t)f(t,x(t),|x'(t)|)=0$, 0< t<1, $x'(0)-{\delta}x(\xi)=0,\;x'(1)+{\delta}x(\eta)=0$, where $\phi_p$ (s) = |s|$^{p-2}$, p > $\delta$ > 0, 1 > $\eta$ > $\xi$ > 0, ${\xi}+{\eta}$ = 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interesting point is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.715-725
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• 2013

In this paper, a finite difference scheme for a two-point boundary value problem of 2nth-order ordinary differential equations is presented. The convergence and uniqueness of the solution for the scheme are proved by means of theories on matrix eigenvalues and norm. Numerical examples show that our method is very simple and effective, and that this method can be used effectively for other types of boundary value problems.

• Journal of KSNVE
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• v.10 no.5
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• pp.800-805
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• 2000

To determine the modal matrix and modal frequency of engine mount system, we most solve so-called eigen-value problem. However eigen-value problem of engine mount system with hydraulic mount can not be solved by general eigne-analysis algorithm because the properties of hydraulic mount vary with frequency. so in this paper the method for modal analysis of rigid body motions of an engine supported by hydraulic mount is proposed. Natural frequencies and mode shapes of this nonlinear system are obtained by using complex exponential method and Laplace transformation method. In time domain, impulse response functions are calculated by (two-sided) discrete inverse Fourier Transformation of forced frequency response functions achieved by Laplace transformation of the differential equation of motion. Considering the fact that frequency response functions synthesized by modal parameters form proposed method are in good agreement with original FRFs, it is proved that the proposed method is very efficient and useful for the analysis of eigne-value problem of hydraulic engine mount system.

• Journal of The Korean Astronomical Society
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• v.39 no.4
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• pp.147-150
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• 2006

In this paper, initial value problem for dynamical astronomy will be established using parabolic cylindrical coordinates. Computation algorithm is developed for the initial value problem of gravity perturbed trajectories. Applications of the algorithm for the problem of final state predication are illustrated by numerical examples of seven test orbits of different eccentricities. The numerical results are extremely accurate and efficient in predicating final state for gravity perturbed trajectories which is of extreme importance for scientific researches as well as for military purposes. Moreover, an additional efficiency of the algorithm is that, for each of the test orbits, the step size used for solving the differential equations of motion is larger than 70% of the step size used for obtaining its reference final state solution.

• Solar Energy
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• v.8 no.1
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• pp.82-94
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• 1988

The hydrodynamic stability equations for natural convection flows adjacent to a vertical isothermal surface in cold or warm water (Boussinesq or non-Boussinesq situation for density relation), constitute a two-point-boundary-value (eigenvalue) problem, which was solved numerically using the simple shooting and the orthogonal collocation method. This is the first instance in which these stability equations have been solved using a computer code COLSYS, that is based on the orthogonal collocation method, designed to solve accurately two-point-boundary-value problem. Use of the orthogonal collocation method significantly reduces the error propagation which occurs in solving the initial value problem and avoids the inaccuracy of superposition of asymptotic solutions using the conventional technique of simple shooting.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.167-182
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• 2007

The existence of solutions of the following multi-point boundary value problem $${x^{(n)}(t)=f(t,\;x(t),\;x'(t),{\cdots}, x^{(n-2)}(t))+r(t),\;0 is studied. Sufficient conditions for the existence of at least one solution of BVP(*) are established. It is of interest that the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bounds of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.

• Journal of the Ergonomics Society of Korea
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• v.9 no.1
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• pp.29-33
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• 1990

The need for the protection of workers in many industrial workstations has long been recognized, and many type of protective equipment have been devised. In many protective equipment designs, this study set limits to the safety helmet. The direct closed head impact problem was idealized as a linear-damped spring model. This study concerns what properties of helment should afford optimal protection in a direct closed head impact problem. The solution to the problem was achieved through analytic method and numerical computation. The answer was found in terms of 4 parameters : 1) rigidity of shell, 2) viscosity of shell, 3)rigidity of harness, 4) viscosity of harness. The choices are as follows 1) to reduce the rigidity value of harness as small as possible 2) to increase the viscosity value of harness as large as possible. 3) to select the rigidity value of shell sufficient for preventing a breakage.

• Journal of the Korea Society of Computer and Information
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• v.20 no.11
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• pp.105-110
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• 2015

This paper deals with a newly proposed algorithm for stable marriage problem, which I coin threshold algorithm. The proposed algorithm firstly constructs an $n{\times}n$ matrix of the sum of each sex's preference over the members of the opposite sex. It then selects the minimum value from each row and column to designate the maximum value of the selected as the sum threshold $p^*_{ij}$. It subsequently deletes the maximum preference $_{mzx}p_{ij}$ from a matrix derived from deleting $p_{ij}$ > $p^*_{ij}$, until ${\mid}c_i{\mid}=1$ or ${\mid}c_j{\mid}=1$. Finally, it undergoes an optimization process in which the sum preference is minimized. When tested on 7 stable marriage problems, the proposed algorithm has proved to improve on the existing solutions.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.311-327
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• 2016

In this paper, we propose an error embedded Runge-Kutta method to improve the traditional embedded Runge-Kutta method. The proposed scheme can be applied into most explicit embedded Runge-Kutta methods. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, the van der Pol equation and another one having a difficulty for the global error control are numerically solved. Finally, a two-body Kepler problem is also used to assess the efficiency of the proposed algorithm.