• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.461-473
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• 2022

In this paper, we study differential equations arising from the generating functions of the geometric polynomials. We give explicit identities for the geometric polynomials. Finally, we investigate the zeros of the geometric polynomials by using computer.

• Journal of Mechanical Science and Technology
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• 제17권4호
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• pp.538-544
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• 2003

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.

• 물과 미래
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• 제29권3호
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• pp.163-176
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• 1996

균일조도관이 경사지어 설치되어 있을 때, 적정량의 유체를 유송하기 위하여 요구되는 펌프의 동력은 양해법으로 바로 산정할 수 있다. 그러나 펌프의 동력이 기지값으로 주어져 있고 관내 유출률이나 관경을 구하고자 할 때 기존 방법은 상당한 반복과정을 거쳐야 된다. 이러한 경우 유동훈(1995b)은 펌프가 작동치 않는 자연경사관이나 수평관에 펌프만 작동할 때의 균일조도관에 대하여 양해법 산정식을 개발한 바 있다. 본 연구는 그의 연구결과에 기초하여 균일조도 경사관에 펌프가 동시에 작동할 때 반복 시산과정을 거치지 않고 관내 유출률이나 관경을 양해법으로 바로 산정하는 수식을 개발하여 제시하였다. 양해법 산정식의 선택에 있어 관로흐름의 수리특성을 다섯가지로 구분하여 각 수리 특성구간의 경계조건식도 양해법으로 도출하였다. 또한 개발된 양해법 근사식을 간단한 설계예에 적용하여 계산의 효율성과 정확성을 확인하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.224-261
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• 2021

The interest in implicit-explicit (IMEX) integration methods has emerged as an alternative for dealing in a computationally cost-effective way with stiff ordinary differential equations arising from practical modeling problems. In this paper, we introduce implicit-explicit second derivative linear multi-step methods (IMEX SDLMM) with error control. The proposed IMEX SDLMM is based on second derivative backward differentiation formulas (SDBDF) and recursive SDBDF. The IMEX second derivative schemes are constructed with order p ranging from p = 1 to 8. The methods are numerically validated on well-known stiff equations.

• 대한수학회논문집
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• 제36권3호
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• pp.549-555
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• 2021

We show the solvability of the ordinary differential equations describing curves on sphere or hyperbolic space. Making use of the geometric properties of the equations, we derive explicit solution formulae.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.341-378
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• 1997

We consider three classes of numerical methods for solv-ing the semi-explicit differential-algebraic equations of index 1 and higher. These methods use implicit multistep fixed stepsize methods and several iterative processes including simple iteration, full a2nd modified Newton iteration. For these methods we prove convergence theorems and derive error estimates. We consider different ways of choosing initial approximations for these iterative methods and in-vestigate their efficiency in theory and practice.

• Structural Engineering and Mechanics
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• 제18권4호
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• pp.411-428
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• 2004

In this study, a newly developed unconditionally stable explicit method is employed to solve momentum equations of motion in performing pseudodynamic tests. Due to the explicitness of each time step this pseudodynamic algorithm can be explicitly implemented, and thus its implementation is simple when compared to an implicit pseudodynamic algorithm. In addition, the unconditional stability might be the most promising property of this algorithm in performing pseudodynamic tests. Furthermore, it can have the improved properties if using momentum equations of motion instead of force equations of motion for the step-by-step integration. These characteristics are thoroughly verified analytically and/or numerically. In addition, actual pseudodynamic tests are performed to confirm the superiority of this pseudodynamic algorithm.

• 대한기계학회논문집B
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• 제21권2호
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• pp.202-212
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• 1997

In this study, performance of the multi-stage explicit methods for numerical computation of the unsteady Navier-Stokes equations is investigated. Three methods under consideration are 1 st-, 2 nd-, and 4 th-order Runge-Kutta (R-K) methods. Compared in this estimation is stability, accuracy, and CPU time of each method. The computational codes developed are applied to the two-dimensional flow in a square cavity driven by an oscillating lid. It turned out that at Reynolds number 400, the 1 st-order R-K method is the best, while at 3200 the 2 nd-order R-K is recommended. At higher Reynolds numbers, it is conjectured that the 4 th-order R-K method will be the best algorithm among three due to its highest stability.

• Journal of information and communication convergence engineering
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• 제12권1호
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• pp.39-45
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• 2014

A numerical method for solving Hamiltonian equations is said to be symplectic if it preserves the symplectic structure associated with the equations. Various symplectic methods are widely used in many fields of science and technology. A symplectic method preserves an approximate Hamiltonian perturbed from the original Hamiltonian. It theoretically supports the effectiveness of symplectic methods for long-term integration. Although it is also related to long-term integration, numerical stability of symplectic methods have received little attention. In this paper, we consider explicit symplectic methods defined for Hamiltonian equations with Hamiltonians of the special form, and study their numerical stability using the harmonic oscillator as a test equation. We propose a new stability criterion and clarify the stability of some existing methods that are visually based on the criterion. We also derive a new method that is better than the existing methods with respect to a Courant-Friedrichs-Lewy condition for hyperbolic equations; this new method is tested through a numerical experiment with a nonlinear wave equation.

• 한국수자원학회논문집
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• 제30권5호
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• pp.495-501
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• 1997

펌프동력이 기지 값으로 주어져 있을 때, 유량이나 관경을 산정하는 경우 기존의 방법으로는 상당한 반복과정을 거쳐야 된다. 이에 유동훈과 강찬수(1996)는 균일조도 동력경사관인 경우 유량인 관경을 양해법으로 산정하는 식을 개발한 바 있다. 마찰계수 산정을 위한 지수함수식의 이용은 본 양해법 산정식의 개발을 가능하게 하였다. 유동훈(1995a)은 상용관이나 복합면을 가진 관의 마찰계수 산정을 위한 마찰계수 평균법을 제시한 바 있다. 그와 같은 접근방법으로 본고는 마찰계수 평균법을 상용관 마찰계수 산정식에 적용하여 동력경사 상용관의 유량이나 관경을 양해법으로 구할 수 있는 산정식을 개발하였다.