• Journal of the Korean Solar Energy Society
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• v.37 no.5
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• pp.77-84
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• 2017

The purpose of this paper is to propose the way of computing conduction time series factors (CTSF) using numerical method. After the accuracy of the numerical solution procedure being verified, the method is applied to the wall type 24 and roof type 14 of ASHARE to find the conduction time series coefficients, so called conduction time series factors. The results agree well with the values presented in the ASHRAE handbook. The method proposed can be easily applied to find unknown CTSF for more complex structures. It provides information about the temperature changes at a given location and time, thus validity of generated CTSF can be checked easily.

• Journal of KSNVE
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• v.5 no.3
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• pp.345-352
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• 1995

A very simple and computationally efficient numerical method is developed for the free vibration of arbitrary shape plates. A set of two- dimensional simple series functions is used as an admissible displacement functions in the Rayleigh-Ritz method to obtain the natural frequencies for the arbitrary shape plates. From the prescribed starting function satisfying only the geometric boundary conditions, the higher terms in the series function are constructed with adding order of polynomial. Natural frequencies are obtained for the arbitrary shape plates, with combinational boundary conditions. The obtained numerical results are presented, some cases are verified with other numerical methods in the literature.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.5 no.3
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• pp.43-50
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• 2006

In this successive study, the analytical realization of coupled system was introduced using the times series identification and spectrum analysis, which was compared with conventional FFT spectrum. Also, the numerical responses of second order system, which is coupled, were solved using the numerical calculation of Runge-Kutta Gill method. After numerical analysis, the displacement, velocity and acceleration were acquired. Among them, the response of displacement was used for the analysis of time series spectrum. Among several time series, the ARMAX algorithm was proved to be appropriate for the spectrum analysis of the coupled system. Using the separated response of 1st and 2nd mode, the mode was calculated separately. And the responses of mixed modes were also analyzed for calculation of the mixed modes in the coupled system.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.173-185
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• 2014

In the present paper, we consider an anomalous diffusion problem in two dimensional space involving Caputo time and Riesz-Feller fractional derivatives and then solve it by using a series involving bilateral eigen-functions. Also, we obtain a numerical approximation formula of this problem and discuss some of its particular cases.

• Structural Engineering and Mechanics
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• v.8 no.4
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• pp.343-360
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• 1999

This work applies a structural analysis method based on an analytical solution from the Fourier series which transforms a half-range cosine expansion into a static solution involving plated structures. Two sub-matrices of in-plane and plate-bending problems are also formulated and coupled with the prescribed boundary conditions for these variables, thereby providing a convenient basis for a numerical solution. In addition, the plate connection are introduced by describing the connection between common boundary continuity and equilibrium. Moreover, a simple computation scheme is proposed. Numerical results are then compared with finite element results, demonstrating the numerical scheme's versatility and accuracy.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.28 no.2
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• pp.228-239
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• 1992

The purpose of the present research is to develop an efficient numerical method for the calculation of potential flow and predict the wave-making resistance for the application to ship design of tuna purse seiner. The paper deals with the numerical calculation of potential flow around the series 60 with forward velocity by the new slender ship theory. This new slender ship theory is based on the asymptotic expression of the Kelvin-source, distributed over the small matrix at each transverse section so as to satisfy the approximate hull boundary condition due to the assumption of slender body. Some numerical results for series 60, C sub(b) =0.6, hull are presented in this paper. The wave pattern and wave resistance are computed at two Froude numbers, 0.267 and 0.304. These results are better than those of Michell's thin ship theory in comparison with measured results. However, it costs much time to compute not only wave resistance but also wave pattern over some range of Froude numbers. More improvements are strongly desired in the numerical procedure.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1055-1071
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• 2010

Recently, a number of algorithms have been proposed for numerical evaluation of Hankel transforms as these transforms arise naturally in many areas of science and technology. All these algorithms depend on separating the integrand $rf(r)J_{\upsilon}(pr)$ into two components; the slowly varying component rf(r) and the rapidly oscillating component $J_{\upsilon}(pr)$. Then the slowly varying component rf(r) is expanded either into a Fourier Bessel series or various wavelet series using different orthonormal bases like Haar wavelets, rationalized Haar wavelets, linear Legendre multiwavelets, Legendre wavelets and truncating the series at an optimal level; or approximating rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. The purpose of this communication is to take a different approach and replace rapidly oscillating component $J_{\upsilon}(pr)$ in the integrand by its Bernstein series approximation, thus avoiding the complexity of evaluating integrals involving Bessel functions. This leads to a very simple efficient and stable algorithm for numerical evaluation of Hankel transform.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.71-82
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• 2023

In this article, we find the approximate solutions of Abel differential equation (ADE) with uncertainty using residual power series (RPS) method. This method helps to calculate the sequence of solutions of ADE. Finally, numerical illustrations demonstrate the applicability of the method.

• Bulletin of the Korean Chemical Society
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• v.10 no.6
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• pp.529-535
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• 1989

A general perturbation series solution of the Smoluchowski equation is applied to investigate the rate of recombination and the remaining probability of a pair of particles in liquids. The radiative boundary condition is employed and the convergence of the perturbation series is analyzed in terms of a convergene factor in time domain. The upper bound to the error introduced by the n-th order perturbation scheme is also evaluated. The long time behaviors of the rate of recombination and the remaining probability are found to be expressed in closed forms if the perturbation series is convergent. A new and efficient method of purely numerical integration of the Smoluchowski equation is proposed and its results are compared with those obtained by the perturbation method. For the two cases where the interaction between the particles is given by (i) the Coulomb potential and (ii) the shielded Coulomb potential, the agreement between the two results is found to be excellent.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.583-593
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• 2022

Lienard's equations are important nonlinear differential equations with application in many areas of applied mathematics. In the present article, a new approach known as the modified fractional Taylor series method (MFTSM) is proposed to solve the nonlinear fractional Lienard equations with Caputo fractional derivatives, and the convergence of this method is established. Numerical examples are given to verify our theoretical results and to illustrate the accuracy and effectiveness of the method. The results obtained show the reliability and efficiency of the MFTSM, suggesting that it can be used to solve other types of nonlinear fractional differential equations that arise in modeling different physical problems.