• 대한수학회보
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• 제50권1호
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• pp.275-283
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• 2013

In this paper we investigate an initial boundary value problem of a logarithmic wave equation. We establish the global existence of weak solutions to the problem by using Galerkin method, logarithmic Sobolev inequality and compactness theorem.

• 대한수학회논문집
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• 제30권3호
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• pp.201-208
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• 2015

This paper reviews recent mathematical progresses made on the study of the initial-value problem for nonlinear Dirac equations in one space dimension. We also prove the global existence of solutions to some nonlinear Dirac equations and propose a model problem (3.6).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권4호
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• pp.221-237
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• 2013

In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.

• Kyungpook Mathematical Journal
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• 제52권2호
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• pp.167-177
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• 2012

In this article, we propose exponentially fitted error correction methods(EECM) which originate from the error correction methods recently developed by the authors (see [10, 11] for examples) for solving nonlinear stiff initial value problems. We reduce the computational cost of the error correction method by making a local approximation of exponential type. This exponential local approximation yields an EECM that is exponentially fitted, A-stable and L-stable, independent of the approximation scheme for the error correction. In particular, the classical explicit Runge-Kutta method for the error correction not only saves the computational cost that the error correction method requires but also gives the same convergence order as the error correction method does. Numerical evidence is provided to support the theoretical results.

• 전기의세계
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• 제21권3호
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• pp.48-52
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• 1972

The application of pontryagin's Maximum Principle to the optimal control eventually leads to the problem of solving the two point boundary value problem. Most of problems have been related to their own special factors, therfore it is very hard to recommend the best method of deriving their optimal solution among various methods, such as iterative Runge Kutta, analog computer, gradient method, finite difference and successive approximation by piece-wise linearization. The gradient method has been applied to the optimal control of two point boundary value problem in the power systems. The most important thing is to set up some objective function of which the initial value is the function of terminal point. The next procedure is to find out any global minimum value from the objective function which is approaching the zero by means of gradient projection. The algorithm required for this approach in the relevant differential equations by use of the Runge Kutta Method for the computation has been established. The usefulness of this approach is also verified by solving some examples in the paper.

• 항공우주기술
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• 제13권2호
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• pp.60-65
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• 2014

본 논문에서는 적분 행렬을 이용한 수치적분 방법을 연구하였다. 비선형 운동방정식에 대한 빠른 수치적분을 수행하기 위해, 적분 행렬을 이용한 개선된 fixed point iteration 방법을 소개한다. 예제로는 궤도 운동에 대한 수치적분 예를 고려한다. 수치 예제를 통하여, 본 논문에서 연구되는 알고리듬이 적분의 정밀도는 크게 저하시키지 않음과 동시에, 계산시간 측면에서 효과적이라는 것을 보인다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.441-448
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• 2000

An investigation into the nonlinear free vibrations of a cantilever beam which can have not only planar motion but also nonplanar motion is made. Using Galerkin's method based on the first mode in each motion, we transform the boundary and initial value problem into an initial value problem of two-degree-of-freedom system. The system turns out to have two normal modes. By Synge's stability concept we examine the stability of each mode. In order to check validity of the stability we obtain the numerical Poincare map of the motions neighboring on each mode.

• International journal of advanced smart convergence
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• 제2권1호
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• pp.18-20
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• 2013

The significance, is to introduce a novel way to employ the improved Runge-Kutta fifth order five stage method, here after called as Modified IRK(5,5) method, for system of second order robot arm problem and variations in angles at the joints in which parameters governing with two degrees of freedom which requires lesser number of function evaluations per time step as compared to the existing ones, in order to save time and spaceAn ultimate aim of this present paper is to solve application problem such as robot arm and initial value problems by applying Runge-Kutta fifth order five stage numerical techniques. The calculated output for robot arm coincides with exact solution which is found to be better, suitable and feasible for solving real time problems.

• 대한수학회보
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• 제50권3호
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• pp.811-821
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• 2013

We study the initial value problem of the exponential wave equation in $\math{R}^{n+1}$ for small initial data. We shows, in the case of $n=1$, the global existence of solution by applying the formulation of first order quasilinear hyperbolic system which is weakly linearly degenerate. When $n{\geq}2$, a vector field method is applied to show the stability of a trivial solution ${\phi}=0$.

• 한국항해학회지
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• 제24권5호
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• pp.361-371
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• 2000

This paper treats a genetic algorithm for ship scheduling problem in set packing formulation. We newly devised a partition based representation of solution and compose initial population using a domain knowledge of problem which results in saving calculation cost. We established replacement strategy which makes each individual not to degenerate during evolutionary process and applied adaptive mutate operator to improve feasibility of individual. If offspring is feasible then an improve operator is applied to increase objective value without loss of feasibility. A computational experiment was carried out with real data and showed a useful result for a large size real world problem.