• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.269-282
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• 2007

In this paper, we consider a two-dimensional fractional space-time diffusion equation (2DFSTDE) on a finite domain. We examine an implicit difference approximation to solve the 2DFSTDE. Stability and convergence of the method are discussed. Some numerical examples are presented to show the application of the present technique.

• 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.

• 대한수학회보
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• 제44권1호
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• pp.13-29
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• 2007

In this paper, we first present a method for finding the implicit equation of the curve given by rational parametric equations. The method is based on the computation of $Gr\"{o}bner$ bases. Then, another method for implicitization of curve and surface is given. In the case of rational curves, the method proceeds via giving the implicit polynomial f with indeterminate coefficients, substituting the rational expressions for the given curve and surface into the implicit polynomial to yield a rational expression $\frac{g}{h}$ in the parameters. Equating coefficients of g in terms of parameters to 0 to get a system of linear equations in the indeterminate coefficients of polynomial f, and finally solving the linear system, we get all the coefficients of f, and thus we obtain the corresponding implicit equation. In the case of polynomial surfaces, we can similarly as in the case of rational curves obtain its implicit equation. This method is based on characteristic set theory. Some examples will show that our methods are efficient.

• 호남수학학술지
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• 제45권1호
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• pp.1-24
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• 2023

In the present paper, we prove common fixed point theorems for a pair of weakly compatible mappings under implicit contractive relation in quasi-partial S_b-metric spaces. We also provide an illustrative example to support our results. Furthermore, we will use the results obtained for application to two boundary value problems for the second-order differential equation. Also, we prove a common solution for the nonlinear fractional differential equation.

• 충청수학회지
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• 제26권3호
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• pp.501-516
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• 2013

The well-known Vlasov-Poisson equation describes plasma physics as nonlinear first-order partial differential equations. Because of the nonlinear condition from the self consistency of the Vlasov-Poisson equation, many problems occur: the existence, the numerical solution, the convergence of the numerical solution, and so on. To solve the problems, a viscosity term (a second-order partial differential equation) is added. In a viscosity term, the Vlasov-Poisson equation changes into a parabolic equation like the Fokker-Planck equation. Therefore, the Schauder fixed point theorem and the classical results on parabolic equations can be used for analyzing the Vlasov-Poisson equation. The sequence and the convergence results are obtained from linearizing the Vlasove-Poisson equation by using a fixed point theorem and Gronwall's inequality. In numerical experiments, an implicit first-order scheme is used. The numerical results are tested using the changed viscosity terms.

• Tribology and Lubricants
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• 제16권4호
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• pp.295-301
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• 2000

The dynamic simulation of slider in hard disk drive is performed using Factored Implicit Finite Difference method. The modified Reynolds equation with Fukui and Kaneko model is employed as a governing equation. Equations of motion for the slider of three degrees of freedom are solved simultaneously with the modified Reynolds equation. The transient responses of the slider for disk step bumps and slider impulse forces are shown for various cases and are compared for the iteration algorithm and new algorithm.

• Journal of Information Processing Systems
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• 제14권5호
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• pp.1068-1074
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• 2018

In this paper, we consider the delay partial differential equation of three dimensions with constant coefficients. We established the alternating direction difference scheme by the standard finite difference method, gave the order of convergence of the format and the expression of the difference scheme truncation errors.

• 한국전산유체공학회지
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• 제2권2호
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• pp.26-34
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• 1997

An implicit viscous turbulent flow solver is developed for two-dimensional geon unstructured triangular meshes. The flux terms are discretized based on a cell-centered formulation with the Roe's flux-difference splitting. The solution is advanced in time us backward-Euler time-stepping scheme. At each time step, the linear system of equation approximately solved wi th the Gauss-Seidel relaxation scheme. The effect of turbulence is with a standard k-ε two-equation model which is solved separately from the mean flow equation the same backward-Euler time integration scheme. The triangular meshes are generated advancing-front/layer technique. Validations are made for flows over the NACA 0012 airfoil. Douglas 3-element airfoil. Good agreements are obtained between the numerical result experiment.

• 한국정보통신학회논문지
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• 제8권3호
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• pp.702-707
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• 2004

본 논문은 CCD 카메라와 거리 센서를 사용하여 컨테이너의 자세 측정에 관하여 연구하였다. 특히 특징점을 추출하고 영상의 잡음을 줄이는 방법에 대하여 중점적으로 기술하였다. 가우시안 및 랜덤 노이즈를 제거하기 위하여 Euler-Lagrange 방정식을 소개하였으며 PDE(Partial Differential Equation)를 기초로 한 Euler-Lagrange 방정식을 풀기 위하여 ADI(Alternating Direction Implicit)방법을 적용하였다. 그리고 스프레더와 컨테이너의 특징점을 추출하기 위해서 기존의 황금 분할법과 이분 분할법을 이용한 방법은 지역적 최대 및 최소 값의 경우 정확한 해를 구할 수 없어서 k차 곡률 알고리즘을 이용하였다. 제안된 알고리즘은 영상의 전처리과정에서 잡음제거에 효과적이며 카메라와 거리센서를 이용한 제안 시스템은 기존시스템의 구조적 변경 없이 사용가능하기 때문에 비용이 저렴한 장점이 있다.

• 대한기계학회논문집A
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• 제27권11호
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• pp.1907-1916
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• 2003

During decades, there has been much progress in understanding of the inelastic behavior of the materials and numerous inelastic constitutive equations have been developed. The complexity of these constitutive equations generally requires a stable and accurate numerical method. To obtain the increment of state variable, its evolution laws are linearized by several approximation methods, such as general midpoint rule(GMR) or general trapezoidal rule(GTR). In this investigation, semi-implicit integration schemes using GTR and GMR were developed and implemented into ABAQUS by means of UMAT subroutine. The comparison of integration schemes was conducted on the simple tension case, and simple shear case and nonproportional loading case. The fully implicit integration(FI) was the most stable but amplified the truncation error when the nonlinearity of state variable is strong. The semi-implicit integration using GTR gave the most accurate results at tension and shear problem. The numerical solutions with refined time increment were always placed between results of GTR and those of FI. GTR integration with adjusting midpoint parameter can be recommended as the best integration method for viscoplastic equation considering nonlinear kinematic hardening.