• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.157-164
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• 2021

Recently we investigated a type of Hyers-Ulam stability of the Schrödinger equation with the symmetric parabolic wall potential that efficiently describes the quantum harmonic oscillations. In this paper we study a type of Hyers-Ulam stability of the Schrödinger equation when the potential barrier is a quartic wall in the solid crystal models.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.29-51
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• 2004

In this paper, we propose a new mixed finite element method, called the characteristics-mixed method, for approximating the solution to Burgers' equation. This method is based upon a space-time variational form of Burgers' equation. The hyperbolic part of the equation is approximated along the characteristics in time and the diffusion part is approximated by a mixed finite element method of lowest order. The scheme is locally conservative since fluid is transported along the approximate characteristics on the discrete level and the test function can be piecewise constant. Our analysis show the new method approximate the scalar unknown and the vector flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. Numerical example is presented to show that the new scheme is easily implemented, shocks and boundary layers are handled with almost no oscillations. One of the contributions of the paper is to show how the optimal error estimates in $L^2(\Omega)$ are obtained which are much more difficult than in the standard finite element methods. These results seem to be new in the literature of finite element methods.

• 한국측량학회지
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• 제30권6_2호
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• pp.593-605
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• 2012

LiDAR systems provide dense and accurate topographic information. A pre-requisite to achieving the potential accuracy of LiDAR is having a proper system calibration, which aims at estimating all the systematic errors in the system measurements and the mounting parameters relating the different components. This paper presents a rigorous and two approximate methods for LiDAR system calibration. The rigorous approach makes use of the LiDAR equation and the system raw measurements. The approximate approaches utilize simplified LiDAR equations using some assumptions, which allow for less strict requirements regarding the raw measurements. The first presented approximate method, denoted as quasi-rigorous, assumes that we are dealing with a vertical platform (i.e., small pitch and roll angles). This method requires time-tagged point cloud and trajectory position data. The second approximate method, denoted as simplified, assumes that we are dealing with parallel strips, vertical platform, and minor terrain elevation variations compared to the flying height above ground. Such method can be performed using the LiDAR point cloud only. Experimental results using a real dataset, whose characteristics deviate to some extent from the utilized assumptions in the approximate methods, are presented to provide a comparative analysis of the outcome from the introduced methods.

• 전자공학회논문지A
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• 제33A권11호
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• pp.120-127
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• 1996

In the WKB analysis, we propose the new forms of the trial eigenfunctions which not only converge at the turning points but also approximate to the conventional WKB solutions away from the turning points. The eigenvalue equation of multiple waveguides with graded index profile are derived by using the proposed WKB analysis and the transfer matrix method. The drived equation sare represented in the recursive form. The results of the eigenvalue equation sare comapred with those of the FDM, one of the well-known computational methods, for a three-waveguide coupler.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.571-579
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• 2007

Finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with a periodic boundary condition, which is of the type $ut+\frac{{\partial}^2} {{\partial}x^2}\;g\;(u,\;u_x,\;u_{xx})=f(u,\;u_x,\;u_{xx})$. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Bulletin of the Korean Chemical Society
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• 제31권12호
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• pp.3573-3578
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• 2010

Recently it is suggested that it may be possible to obtain the approximate or exact bound state solutions of nonrelativistic Schr$\ddot{o}$dinger equation from relativistic Klein-Gordon equation, which seems to be counter-intuitive. But the suggestion is further elaborated to propose a more detailed method for obtaining nonrelativistic solutions from relativistic solutions. We demonstrate the feasibility of the proposed method with the Morse potential as an example. This work shows that exact relativistic solutions can be a good starting point for obtaining nonrelativistic solutions even though a rigorous algebraic method is not found yet.

• 대한수학회지
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• 제38권3호
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• pp.657-667
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• 2001

We propose a statistical interpolation approximate solution for a nonlinear stochastic integral equation of a stock price process. The proposed method has the order O(h$^2$) of local error under the weaker conditions of $\mu$ and $\sigma$ than those of Milstein' scheme.

• 한국해안해양공학회지
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• 제18권4호
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• pp.360-371
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• 2006

천해역의 파랑을 추산하기 위한 포물형 근사식에 대해 기존 모형을 도출할 수 있는 일반화된 모형을 제시하고 이를 수정 완경사 파랑식에 대한 포물형 근사식으로 확장하였다. 제시한 수치모형을 Berkhoff et al.(1982)의 수리모형 실험과 비교하였으며 이 경우에는 기존 포물형 근사모형과 수정 포물형 근사모형의 결과가 거의 같으며 수리실험 결과와 아주 잘 일치하는 것으로 나타났다. 따라서 계산이 빠르고 안정성이 높은 기존 포물형 근사식은 천해역의 파랑 추산에 유용한 도구라 판단된다.

• 한국음향학회지
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• 제18권4호
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• pp.71-77
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• 1999

본 논문에서는 거리종속 해양에서 음전달 풀이법으로 각광받고 있는 포물선 방정식법에 대한 고차 해의 전산코드를 작성하고 이들에 대한 수치 시험을 수행하였으며 포물선 방정식법의 정확성을 수치문제 적용 측면에서 고찰하였다. 깊이 방향 연산자의 선형 근사방법으로는 (equation omitted) 근사법의 곱형태를 이용하였으며 Galerkin방법을 이용하여 수치계산을 수행하였고 계산량의 감소를 위하여 부분적으로 collocation을 이용하였다. 거리방향 연산자는 음해법인 Crank-Nicolson법, 초기해로는 자체 초기해를 이용하였다. 수치시험은 세 가지 해양 환경에 대하여 시행하였고 이들의 결과는 해석해, 파수적분법을 이용한 OASES결과와 기존의 포물선 방정식법을 이용한 전산조직인 RAM 등과 비교하였다.

• Ecology and Resilient Infrastructure
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• 제1권1호
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• pp.1-7
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• 2014

본 연구에서는 파랑과 흐름이 공존하고 있는 해안지역에 이용이 가능한 물에 용해된 물질의 정확한 이동을 예측하기 위한 수심적분형 수치모의 기법을 제시한다. 대상 영역에 일반적으로 발생하는 파랑의 전파와 변형 과정 및 쇄파와 흐름의 발달 과정에 대한 모의가 가능한 boussinesq equation 흐름모형과 동일한 과정을 거쳐 유도된 수심적분형 물질수송모형을 지배방정식으로 이용한다. 지배방정식은 approximate riemann solver를 이용하는 유한체적법을 이용하여 해석한다. 제시된 수치모형을 이용하여 해일발생에 의한 흐름양상을 계측한 실험을 재현하였으며, 해당 수역에 가상의 물질의 이송과 확산에 대한 수치모의를 수행하고 그 결과를 분석하였다.