• International Journal of Aeronautical and Space Sciences
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• 제18권4호
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• pp.816-826
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• 2017

In this paper, a generalized discretization scheme is proposed that can derive general-order finite difference equations representing the joint probability density function of dynamic response of stochastic systems. The various order of finite difference equations are applied to solutions of the Fokker-Planck-Kolmogorov (FPK) equation. The finite difference equations derived by the proposed method can greatly increase accuracy even at the tail parts of the probability density function, giving accurate reliability estimations. Compared with exact solutions and finite element solutions, the generalized finite difference method showed increasing accuracy as the order increases. With the proposed method, it is allowed to use different orders and types (i.e. forward, central or backward) of discretization in the finite difference method to solve FPK and other partial differential equations in various engineering fields having requirements of accuracy or specific boundary conditions.

• Structural Engineering and Mechanics
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• 제17권6호
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• pp.735-749
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• 2004

This work presents a direct integration scheme, based on a fourth order finite difference approach, for elastodynamics. The proposed scheme was chosen as an alternative for attenuating the errors due to the use of the central difference method, mainly when the time-step length approaches the critical time-step. In addition to eliminating the spurious numerical oscillations, the fourth order finite difference scheme keeps the advantages of the central difference method: reduced computer storage and no requirement of factorisation of the effective stiffness matrix in the step-by-step solution. A study concerning the stability of the fourth order finite difference scheme is presented. The Finite Element Method and the Boundary Element Method are employed to solve elastodynamic problems. In order to verify the accuracy of the proposed scheme, two examples are presented and discussed at the end of this work.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.299-309
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• 2013

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method (FChFD). The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. We tested this technique to solve numerically fractional BVPs. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The fractional derivatives are presented in terms of Caputo sense. The application of the method to fractional BVPs leads to algebraic systems which can be solved by an appropriate method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회B
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• pp.2254-2255
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• 2008

Thermoforming is one of the most versatile and economical process to produce polymer products. The drawback of thermoforming is difficult to control thickness of final products. Temperature distribution affects the thickness distribution of final products, but temperature difference between surface and center of sheet is difficult to decrease because of low thermal conductivity of ABS material. In order to decrease temperature difference between surface and center, heating profile must be expressed as exponential function form. In this study, Finite Difference Method was used to find out the coefficients of optimal heating profiles. Through investigation, the optimal results using Finite Difference Method show that temperature difference between surface and center of sheet can be remarkably minimized with satisfying Temperature of Forming Window.

• Journal of Korea Trade
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• 제24권5호
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• pp.1-17
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• 2020

Purpose - This paper tries to estimate the effects of China's and Japan's free trade agreement (FTA) by panel generalized least squares (GLS). Design/methodology - The GLS model includes the basic gravity theory and Difference in Difference (DD) method to divide FTA conclusion countries and non-FTA conclusion countries with China and Japan. In order to empirically research the difference between Chinese and Japanese FTAs, we use the Difference in Difference in Difference (DDD) method. Findings - This paper finds the distance variable has more influence on Japanese than Chinese trade. The exchange rate indicates that Chinese trade depends on export and Japanese trade has the structure of re-import; shows that the countries that concluded FTAs with China and Japan have more positive trade effects than those that did not; finds the Chinese FTA promotion effects greater than the Japanese FTA because China had pushed ahead with trade policy since joining the WTO in 2001. Originality/value - This study shows that a single country's FTA and trade policies are an important factor concerning not just the promotion of trade but also the issue of trade conflicts.

• Structural Engineering and Mechanics
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• 제53권2호
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• pp.249-260
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• 2015

Damage detection based on a reference set of measured data usually has the problem of different environmental temperature in the two sets of measurements, and the effect of temperature difference is usually ignored in the subsequent model updating. This paper attempts to identify the structural damage including the temperature difference with artificial measurement noise. Both local damages and the temperature difference are identified in a gradient-based model updating method based on dynamic response sensitivity. The sensitivities of dynamic response with respect to the system parameters and temperature difference are calculated by direct integration method. The measured dynamic responses of the structure from two different states are used directly to identify the structural local damages and the temperature difference. A single degree-of-freedom mass-spring system and a planar truss structure are studied to illustrate the effectiveness of the proposed method.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.501-506
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• 2007

A generalized finite difference method for solving solid mechanics problems such as elasticity and crack problems is presented. The method is constructed in framework of Taylor polynomial based on the Moving Least Squares method and collocation scheme based on the diffuse derivative approximation. The governing equations are discretized into the difference equations and the nodal solutions are obtained by solving the system of equations. Numerical examples successfully demonstrate the robustness and efficiency of the proposed method.

• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.135-154
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• 2018

In this paper, an almost second order overlapping Schwarz method for singularly perturbed third order convection-diffusion type problem is constructed. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the combination of classical finite difference scheme and central finite difference scheme on a uniform mesh while on the non-layer region we use the midpoint difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. We proved that, when appropriate subdomains are used, the method produces convergence of second order. Furthermore, it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme are it reduce iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• Nuclear Engineering and Technology
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• 제50권3호
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• pp.327-339
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• 2018

This article presents a new global-local hybrid coarse-mesh finite difference (HCMFD) method for efficient parallel calculation of pin-by-pin heterogeneous core analysis. In the HCMFD method, the one-node coarse-mesh finite difference (CMFD) scheme is combined with a nodal expansion method (NEM)-based two-node CMFD method in a nonlinear way. In the global-local HCMFD algorithm, the global problem is a coarse-mesh eigenvalue problem, whereas the local problems are fixed source problems with boundary conditions of incoming partial current, and they can be solved in parallel. The global problem is formulated by one-node CMFD, in which two correction factors on an interface are introduced to preserve both the surface-average flux and the net current. Meanwhile, for accurate and efficient pin-wise core analysis, the local problem is solved by the conventional NEM-based two-node CMFD method. We investigated the numerical characteristics of the HCMFD method for a few benchmark problems and compared them with the conventional two-node NEM-based CMFD algorithm. In this study, the HCMFD algorithm was also parallelized with the OpenMP parallel interface, and its numerical performances were evaluated for several benchmarks.

• 음성과학
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• 제15권3호
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• pp.7-15
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• 2008

This paper proposes the method to extract new feature vectors using the difference between the cepstrum for static characteristics and delta cepstrum for dynamic characteristics in speaker recognition (SR). The difference vector (DV) which it proposes from this paper is containing the static and the dynamic characteristics simultaneously at the intermediate characteristic vector which uses the deference between the static and the dynamic characteristics and as the characteristic vector which is new there is a possibility of doing. Compared to the conventional method, the proposed method can achieve new feature vector without increasing of new parameter, but only need the calculation process for the difference between the cepstrum and delta cepstrum. Experimental results show that the proposed method has a good performance more than 2.03%, on average, compared with conventional method in speaker identification (SI).