• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.10
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• pp.2724-2730
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• 1996

In this paper, the dispersive characteristics of the Finite-Difference Frqequency-Domain method based on the Multi-Resolution Technique(MR-FDFD) are numerically analyzed. A dispersion analysis of the MR-FDFD ority of the MR-FDFD method to the spatial discretization is shown. We expect that the multi-resoluation technique will improve the disavantage of the finite difference techqnique which needs the large comutational memory for accurate electromagnetic analysis.

• Structural Engineering and Mechanics
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• v.46 no.2
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• pp.269-294
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• 2013

This paper is concerned with the determination of exact buckling loads and vibration frequencies of variable thickness isotropic plates using well known finite difference technique. The plates are subjected to uni, biaxial compression and shear loadings and various combinations of boundary conditions are considered. The buckling load is found out as the in plane load that makes the determinant of the stiffness matrix equal to zero and the natural frequencies are found out by carrying out eigenvalue analysis of stiffness and mass matrices. New and exact results are given for many cases and the results are in close agreement with the published results. In this paper, like finite element method, finite difference method is applied in a very simple manner and the application of boundary conditions is also automatic.

• Journal of Environmental Health Sciences
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• v.26 no.3
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• pp.50-54
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• 2000

Ventilation rates can be measured directly by a tracer decay method, although little is known of the effects of different sampling intervals on decay rte calculations. This study determined variations in decay rates calculated by three techniques using residential ozone decay data. The calculation techniques were a regression technique, decay techniques using half-life and average-life, and finite difference techniques using two different time intervals. Variation associated with regression technique calculations for residential ozone decay rates based on data from both sample intervals were within 10% (2.81$\pm$1.88 hr-1). However, both half-life and finite difference technique calculations using a shorter-time interval were significantly different from those obtained with the regression technique(p<0.05). Therefore, the use of short sampling intervals in tracer decay may cause significant error in decay rate calculations.

• ETRI Journal
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• v.45 no.4
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• pp.704-712
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• 2023

This paper presents a flexible finite-difference technique for analyzing the nonuniform guiding structures. Because the voltage and current variations along the nonuniform structure differ for each segment, this work considers the adaptable discretization steps. This technique increases the accuracy of the final response. Moreover, by applying the singular value decomposition and discarding the nonprincipal singular values, an optimal lower rank approximation of the discretization matrix is obtained. The computational cost of the introduced method is significantly reduced using the optimal discretization matrix. Also, the proposed method can be extended to the nonuniform waveguides. The technique is verified by analyzing several practical transmission lines and waveguides with nonuniform profiles.

• Water Engineering Research
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• v.2 no.2
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• pp.75-87
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• 2001

A new moving boundary technique for leap-frog finite difference numerical mode is proposed for the resonable simulation of coastal inundation over discontinuous topography. The new scheme improves the moving boundary technique developed by Imamura(1996). The present scheme is tested using the analytical solution of Thacker(1981) for the case of free oscillation with moving boundary in a parabolic bowl. Finally, a numerical simulation is conducted for the flooding over a tidal barrier constructed on a simple concave geometry. A general feature of inundation over a discontinuous topography is well described by the numerical model.

• Journal of Korean Society of Steel Construction
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• v.12 no.3 s.46
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• pp.303-315
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• 2000

The main object of this study is to analyze mechanical behaviors as anisotropic three-dimensional body under various static loads. This paper presents the applicability of the finite difference method to three dimensional problem of anisotropic body. The finite difference method as applied here is generalized to anisotropic three-dimensional problem of elastic body where the governing differential equations of equilibrium of such bodies are expressed in terms of the displacement u, v, and w in the coordinates axes x, y and z, care being taken to modify the finite difference expressions to satisfy the appropriate boundary conditions. By adopting a new three dimensional finite difference modelling including elimination of pivotal difference points in the case of free boundary condition, the three dimensional problem of anisotropic body was successfully completed. Several numerical results show quick convergence and numerical validity of finite difference technique in three dimensional problem.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.224-227
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• 2001

Adaptive analysis of multilayered composite and sandwich plates is carried out. The adaptive analysis is based on a finite element error form, which measures the difference between the through-the-thickness distribution of finite element displacement and the actual displacement. The region where the error-measure exceeds the prescribed admitted error value, the finite element mesh locally refined in the thickness direction using the mesh superposition technique. Several numerical tests are conducted to validate the effectiveness of the current approach for adaptive analysis of laminated plates.

• Journal of Ocean Engineering and Technology
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• v.10 no.3
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• pp.62-73
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• 1996

Numerical simulation is made of the three-dimensional wave breaking motion about a part of a floating offshore structure containing a circular cylinder mounted vertically onto a lower hull in regular periodic gravity wave generated by a numerical wave maker. TUMMAC-VIII finite-difference method is newly developed for such a problem. By use of density-function technique the three-dimensional wave breaking motion is approximately implenented in the framework of rectangular grid system. A porosity technique is devised for the implementation of the no-slip bydy boundary conditions. The generation of breaking waves by the interaction of incident waves with the structure is well simulated and interesting features of breaking waves are revealed with containing degree of quantitative and qualitative accuracy.

• Journal of Ocean Engineering and Technology
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• v.17 no.6
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• pp.7-15
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• 2003

A Digital Wave Tank simulation technique, based on a finite-difference method and a modified marker-and-cell (MAC) algorithm, is applied in order to investigate the characteristics of nonlinear Tsunami propagations and their interactions with a 2D sloping beach, Ohkushiri Island, and to predict maximum wove run-up around the island. The Navier-Stokes (NS) and continuity equation are governed in the computational domain, and the boundary values are updated at each time step, by a finite-difference time-marching scheme in the frame of the rectangular coordinate system. The fully nonlinear, kinematic, free-surface condition is satisfied by the modified marker-density function technique. The near shore Tsunami is assumed to be a solitary wave, and is generated from the numerical wave-maker in the developed Digital Wave Tank. The simulation results are compared with the experiments and other numerical methods, based on the shallow-water wave theory.