• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.91-98
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• 2005

The straight rectangular fin is analyzed using the one-dimensional analytic method and the finite difference method. For the finite difference method, the numbers of nodes vary from 20 to 100. The relative errors of heat loss and temperature between the analytic method and the finite difference method are represented as a function of Biot Number and dimensionless fin length. One of the results shows that the relative error between the analytic method and the finite difference method decreases as the numbers of nodes for finite difference method increase.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.4
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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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• v.17 no.6
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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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• v.31 no.1_2
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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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.

• Proceedings of the KSME Conference
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• 2008.11b
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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.

• Geophysics and Geophysical Exploration
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• v.22 no.2
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• pp.56-61
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• 2019

In this paper, we studied efficient modeling strategies when we simulate the 3D time-domain acoustic wave propagation using a cell-based finite difference method which can handle the variations of both P-wave velocity and density. The standard finite difference method assigns physical properties such as velocities of elastic waves and density to grid points; on the other hand, the cell-based finite difference method assigns physical properties to cells between grid points. The cell-based finite difference method uses average physical properties of adjacent cells to calculate the finite difference equation centered at a grid point. This feature increases the computational cost of the cell-based finite difference method compared to the standard finite different method. In this study, we used additional memory to mitigate the computational overburden and thus reduced the calculation time by more than 30 %. Furthermore, we were able to enhance the performance of the modeling on several media with limited density variations by using the cell-based and standard finite difference methods together.

• Journal of Technologic Dentistry
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• v.11 no.1
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• pp.83-88
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• 1989

This investigation was performed to evaluate the effect of four different preteatment techniques on the bond strength of porcelain to non-precious metal alloy. Samples of total of 40 were divided into 4 groups according to the 4 variables which included the 50$\mu$alumina oxide air abrasion, method, the as retention bead method, the L-retention bead method, the Etching method. The completed metal-porcelain samples were compressed in Instron loading machine until gross fracture occured to examine the effect of the complex variables on the bond strength of porcelain to non precious metal alloy. The result obtained were as follows : 1. The difference of bond strength according to four different pretreatment techniques was statistically significant(p<0.01). 2. The difference of bond strength between the ss-retention bead method and the L-retention bead method was not significant statistically(p>0.05) 3. The difference of bond strength between the retention bead method and the etching method was statistically significant(p<0.01). 4. The difference of bond strength between the retention bead method and the 50$\mu$alumina oxide air abrasion method was statistically significant(p<0.01). 5. The difference of bond strength between the etching method and the 50$\mu$alumina oxide air abrasion method was statistically significant(p<0.01).

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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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.

• Speech Sciences
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• v.15 no.3
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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).