• Journal of applied mathematics & informatics
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• 제8권3호
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• pp.683-691
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• 2001

A linearized finite-difference scheme is used to transform the initial/boundary-value problem associated with the nonlinear Schrodinger equation into a linear algebraic system. This method is developed by replacing the time and the nonlinear term by an appropriate parametric linearized scheme based on Taylor’s expansion. The resulting finite-difference method is analysed for stability and convergence. The results of a number of numerical experiments for the single-soliton wave are given.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.261-275
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• 2002

Besides asymptotic method, the method of orthogonal polynomials has been used to obtain the solution of the Fredholm integral equation. The principal (singular) part of the kerne1 which corresponds to the selected domain of parameter variation is isolated. The unknown and known functions are expanded in a Chebyshev polynomial and an infinite a1gebraic system is obtained.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.1-28
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• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.241-251
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• 2005

In this paper, we introduce a new algebraic method to characterize rational PH plane curves. And using this method, we study the algebraic characterization of generic strongly regular rational plane PH curves expressed in the complex formalism which is introduced by R.T. Farouki. We prove that generic strongly semi-regular rational PH plane curves are completely characterized by solving a simple functional equation H(f, g) = $h^2$ where h is a complex polynomial and H is a bi-linear operator defined by H(f, g) = f'g - fg' for complex polynomials f,g.

• 한국수학사학회지
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• 제17권3호
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• pp.23-32
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• 2004

본 고에서는 유클리드의 원론에 나타난 대수적 개념들을 개괄하고, 현대적인 기호로 그 의미를 분석하였다. 유클리드의 원론에는 이차방정식, 곱셈공식, 비례식, 정수론, 무리수 등의 대수적 개념이 포함되어 있으나, 그 표현과 추론은 완전히 기하학적인 형태로 이루어져 있다 이러한 내용을 분석하는 것은 대수학의 발생적 본질을 찾아 최초에 수학이 만들어지는 상황을 학생들에게 경험하게 함으로써 수학화를 구현하려는 교육적인 문제의식에도 일종의 시사를 제공하게 될 것이다.

• 한국항공우주학회지
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• 제30권3호
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• pp.8-16
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• 2002

헬리콥터 비행 시뮬레이션을 위한 로터 운동방정식을 implicit formulation 형태로 유도하였다. 좌표계 사이의 상대운동을 고려한 일반화된 벡터 kinematics 를 유도하고 이를 적용하여 브레이드 임의 위치 에서 관성속도 및 관성가속도를 구하였다. 유도된 속도 및 가속도 벡터를 이용하여 플래핑, 리드래그 및 토오크 방정식 등을 implicit form으로 유도하였다. 브레이드 스팬에 따른 공간 적분 방법을 살펴보고, 다양한 힌지형상 및 힌지배열 순서에 관계없이 응용영역을 확장할 수 있음을 밝혔다. DAE(Differential Algebraic Equation) 형태를 갖는 본 연구의 결과식을 이용하여 동특성 계산을 위한 시간적분법을 검토하였다.

• 한국전산구조공학회논문집
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• 제18권2호
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• pp.141-149
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• 2005

본 논문에서는 유연체 동역학해석을 위하여 유한회전을 표현하는데 있어, 4원법의 대수학적인 표현을 도입하여 운동방정식이 에너지보존 조건을 만족하도록 이산화된 에너지 평형식으로 정식화되었다. 여기서 사용된 유한회전의 4원법은 로드리게스 매개변수를 이용하도록 하였으며, 구속력에 대한 일이 제거되도록 하였다. 수치해석의 예를 통하여 제안된 방법이 사다리꼴 방법과 비교할 때 비선형 문제에서도 무조건적으로 안정조건을 보장함을 검증하였으며, 향후 유연한 관절로 연결된 3차원 유연다물체에 대한 동역학 해석을 확장할 수 있는 토대를 마련하였다.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2001년도 추계 학술발표회 논문집 Proceedings of EESK Conference-Fall 2001
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• pp.117-124
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• 2001

A simplified method fur the eigenpair sensitivities of damped system with multiple eigenvalues is presented. This approach employs a reduced equation to determine the sensitivities of eigenpairs of the damped vibratory systems with multiple natural frequencies. In the proposed method, adjacent eigenvectors and orthonormal conditions are used to compute an algebraic equation whose order is (n+m)x(n+m), where n is the number of coordinates and m the number of multiplicity of multiple natural frequencies. The proposed method is an improved Lee and Jung's method which was developed previously. Two equations are used to find eigenvalue derivatives and eigenvector derivatives in Lee and Jung's method. A significant advantage of this approach over Lee and Jung's method is that one algebraic equation newly developed is enough to compute such eigenvalue derivatives and eigenvector derivatives. This method can be consistently applied to both structural systems with structural design parameters and mechanical systems with lumped design parameters. To demonstrate the theory of the proposed method and its possibilities in the case of multiple eigenvalues, the finite element model of the cantilever beam and 5-DOF mechanical system in the case of a non-proportionally damped system are considered as numerical examples. The design parameter of the cantilever beam is its height. and that of the 5-DOF mechanical system is a spring.

• 대한기계학회논문집
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• 제17권6호
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• pp.1596-1608
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• 1993

본 연구에서는 좀더 정량적인 이론에 바탕하여 제레이놀즈수 2차모멘트 난류모형을 유도하려 한다.

• 전자공학회논문지B
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• 제33B권12호
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• pp.84-94
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• 1996

In this work, a fuzzy petri net model for modeling a general form of fuzzy production system which consists of chaining fuzzy production rules and so requires multistage reasoning process is presented. For the obtained fuzzy petri net model, the net will be transformed into some matrices, and also be systematically led to an algebraic form of a state equation. Since it is fond that the approximate reasoning process in fuzzy systems corresponds to the dynamic behavior of the fuzzy petri net, it is further shown that the multistage reasoning process can be carried out by executing the state equation.