• 한국통신학회:학술대회논문집
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• 한국통신학회 2006년도 하계종합학술발표회 논문 초록집
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• pp.574-574
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• 2006

• Journal of Mechanical Science and Technology
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• 제20권5호
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• pp.658-667
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• 2006

Fractional derivative models, which are used to describe the viscoelastic behavior of material, have received considerable attention. Thus it is necessary to put forward the analysis solutions of dynamic systems containing a fractional derivative. Although previously reported such kind of fractional calculus-based constitutive models, it only handles the particularity of rational number in part, has great limitation by reason of only handling with particular rational number field. Simultaneously, the former study has great unreliability by reason of using the complementary error function which can't ensure uniform real number. In this paper, a new approach is proposed for an analytical scheme for dynamic system of a spring-mass-damper system of single-degree of freedom under general forcing conditions, whose damping is described by a fractional derivative of the order $0<{\alpha}<1$ which can be both irrational number and rational number. The new approach combines the fractional Green's function and Laplace transform of fractional derivative. Analytical examples of dynamic system under general forcing conditions obtained by means of this approach verify the feasibility very well with much higher reliability and universality.

• 대한수학회지
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• 제58권3호
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• pp.553-569
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• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.753-765
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• 2020

Smoking is one of the main causes of health problems and continues to be one of the world's most significant health challenges. In this paper, we use the multi-step Adomian decomposition method (MSADM) to obtain approximate analytical solutions for a mathematical fractional model of the evolution of the smoking habit. The proposed MSADM scheme is only a simple modification of the Adomian decomposition method (ADM), in which ADM is treated algorithmically with a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically. The results reveal that the method is effective and convenient for solving linear and nonlinear differential equations of fractional order.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.449-471
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• 2023

In this paper, we study a linear system of homogeneous commensurate /incommensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.

• 대한전자공학회논문지SP
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• 제45권3호
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• pp.74-79
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• 2008

본 논문은 H.264/AVC 비디오 코덱의 부화소 움직임 추정 연산을 효율적으로 줄일 수 있는 고속 부화소 움직임 추정 알고리즘을 제안한다. 부화소 움직임 추정 연산은 보다 정확한 움직임 벡터를 찾을 수 있어 비디오 코덱에 널리 사용되지만, 추가적인 보간 및 탐색 연산으로 인해 부호화기의 연산량을 증가시키는 문제점이 있다. 제안하는 고속 부화소 움직임 추정 알고리즘은 SASR(Simplified Adaptive Search Range)을 이용하여 부화소 움직임 추정 연산을 선택적으로 수행하며 MSDSP(Mixed Small Diamond Search Pattern)을 이용하여 부화소 탐색 지점을 감소시켰다. 제안한 알고리즘은 전역 부화소 탐색 알고리즘과 비교하여 탐색 지점이 최대 93.2% 감소하였으며, PDFPS(Prediction-based directional fractional pixel search) 알고리즘보다 탐색 지점이 최대 81% 감소하며 PSNR 감소는 최대 0.04dB로 화질의 열화는 매우 미비했다.

• 한국전산유체공학회지
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• 제8권3호
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• pp.50-55
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• 2003

Recent numerical simulation has a tendency to require the higher-order accuracy in time, as well as in space. This tendency is more true in LES and acoustic noise simulation. In the present work, the accuracy of a Fractional step method, which is widely used in LES simulation, has been increased to the fourth-order accurate compact Pade discretization. To validate the present code, the flow-field past a cylinder was simulated and compared with experiment. A good agreement with experiment was achieved.

• 품질경영학회지
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• 제38권1호
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• pp.42-51
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• 2010

For the fractional factorial designs, the resolution-IV designs can be used when we want to estimate the main effects and to investigate the structure of the non-negligible two-factor interaction effects, when the three-factor and higher order interaction effects are all negligible. However we need to add the additional treatment combinations in order to identify the influential interactions for the resolution-IV fractional factorial designs. In this paper we investigate the statistical structure for 3-level resolution-IV designs constructed by fold-over scheme and introduce a method for analyzing the influential two-factor interactions.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2006년도 하계종합학술대회
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• pp.519-520
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• 2006

In this paper, we propose a voltage-controlled ring oscillator (VCO) for a 900 MHz low-noise fractional-N frequency synthesizer. The VCO delay cell is based on an nMOS source-coupled pair with load elements [1] and a combined tail current sources which consist of a large and a small current source to control the integer and fractional behaviors, respectively. The Spectre simulation results of the scheme in a 0.18um CMOS process show the accurate control of the KVCO better than the conventional one.

• 한국수자원학회논문집
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• 제44권2호
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• pp.145-156
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• 2011

본 연구에서는 자연하천의 흐름에서 흔히 발생하는 천이류, 불연속류, 마른하도로의 파의 전파 등을 포함하는 복잡한 흐름을 해석하기 위한 고정확도 2차원 수치모형을 개발하였다. 하상경사항을 효율적으로 처리하기 위해 quasi-steady wave propagation 기법을 적용하여 해당 격자에 대한 생성항의 영향을 효율적으로 반영함으로써 쌍곡선형 적분 보존형의 2차원 천수방정식을 해석하였다. Fractional Step Method를 적용한 유한체적기법의 사용을 위해 HLL Riemann 해법을 이용하여 흐름률을 계산하였고, 시간 및 공간에 대한 2차 정확도를 만족하기 위해 MUSCL 기법을 적용하였다. 2차 정확도의 사용으로 불연속지점에서 발생하는 수치진동은 TVD 기법 적용을통해 제어하였다. 개발된모형은 2차원 제방 붕괴 및 댐하류부에 구조물이 존재하는 경우의댐 붕괴 모의를 통해실측치와의 검증을 실시하였다. 또한 하류부에 역경사가 존재하는 경우의 댐 붕괴 모의를 통해 실측치와 비교함으로써 생성항의 영향에 대한 모형의 적용성을 검증하였다.