• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• Carbon letters
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• v.1 no.3_4
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• pp.148-153
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• 2001

The initial irreversible capacity, $Q_i$, is one of the parameters to express the material balancing of the cathode to anode. We introduced new terms, which are the initial intercalation Ah efficiency (IIE) and the initial irreversible specific capacity at the surface ($Q_{is}$), to express precisely the irreversibility of an electrode/electrolyte system. Two terms depended on kinds of active-materials and compositions of the electrode, but did not change with charging state. MPCF had the highest value of IIE and the lowest value of $Q_{is}$ in 1M $LiPE_6$/EC + DEC (1 : 1 volume ratio) electrolyte. IIE value of $LiCoO_2$ electrode was 97-98%, although the preparation condition of the material and the electrolyte were different. $Q_{is}$ value of $LiCoO_2$ was 0~1 mAh/g. MPCF-$LiCoO_2$ cell system had the lowest of the latent capacity. $Q_{is}$ value increased slightly by adding conductive material. IIE and $Q_{is}$ value varied with the electrolyte. By introducing PC to EC+DEC mixed solvent, IIE values were retained, but $Q_{is}$ increased. In case of addition of MP, IIE value increased and $Q_{is}$ value also increased a little.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.131-145
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• 2013

In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.79-95
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• 2008

The local existence of solutions for the initial-boundary value problem of a generalized Boussinesq equation on the half line is considered. The approach consists of replacing he Fourier transform in the initial value problem by the Laplace transform and making use of modern methods for the study of nonlinear dispersive wave equation

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.353-361
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• 2022

For an initial value problem, using a weighted average between two adjacent approximates, we propose a simple one-step method based on the Euler method. This method is useful for solving stiff initial value problem, even when the step size is not very small. Moreover, it can be seen that the proposed method with some selected weights results in improved approximation errors.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.53-67
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• 2022

Nonlinear system of initial value problems involving R-L fractional derivative is studied. Monotone iterative technique coupled with lower and upper solutions is developed for the problem. It is successfully applied to study qualitative properties of solutions of nonlinear system of initial value problem when the function on the right hand side is nondecreasing.

• The Korean Journal of Franchise Management
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• v.14 no.4
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• pp.35-50
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• 2023

Purpose: This study aims to uncover the mechanism of how initial fees are determined in the restaurant franchise business. Since the initial fees can be considered as a price of utilizing business models and operational knowledge of a certain franchise brand, it is critical to understand the fee decision-making process based on the strategic pricing theories. Therefore, this study investigates the influence of operational value on the determination of initial franchise fees grounded on a value-based pricing strategy. The Operational value is specifically categorized into profitability, growth, and stability of the franchise system. Research design, data, and methodology: The data used were collected through franchise disclosure documents and brand equity index provided by Korea Management Association Consulting. Data from 44 franchise restaurants during 2018 to 2021 are included in the sample. The panel dataset was analyzed by using generalized least squares estimation with R-Studio. Results: Profitability and stability positively influence initial franchise fees. However, growth did not influence initial franchise fees. Conclusions: The results of the study demonstrate that the operational value plays a critical role in determining the franchise fees. Specifically, franchisees recognize how much revenue a franchise system generates for them (i.e., profitability) and how stable the entire system is for operating business (i.e., stability) when they make purchasing decisions for franchise. The findings extend the pricing literature by applying pricing theories in the franchise fee context. Also, the study contributes to franchising and restaurant management literature by providing knowledge of how franchise fees are determined.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.450-455
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• 1993

Guidance commands for attitude controlled missiles inevitably take the form of attitude angle commands. On the other hand, many guidance laws compute the accelerations required to achieve their goals. Therefore some integrators must be in use for the attitude controlled missiles to implement the guidance laws. Naturally, the use of the integrator raises the problem of choosing a proper initial value. In this paper, we compute the integrator initial value which minimizes the terminal miss and show that if the total flight time of the mission is long enough, the "optimal" initial value becomes some multiple of the initial heading error or of the given impact angle to the target. We demonstrate the validity of the analysis by showing some linear and nonlinear simulation results.n results.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.2
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• pp.284-292
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• 2003

In this paper, we carried out the numerical examination of the initial value setting-up method to extend the range of optimal step parameter in a adaptive system which is controlled by LMS algorithm. For initial value setting-up methods, the general method which select the initial value randomly and the other method which applies the approximate value obtained from the direct method to initial value, were used. And then, we compared to the ranges of step parameter setting, the convergence speeds of mean-square-error, and the stabilities during the convergence process when the initial values were applied to the optimal directivity synthesis problem. According to the numerical simulation results, the initial value setting-up method by means of the direct method provides wider range for the step parameter, more efficient capability for convergence and stability, and more error correction ability than the general method.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1995.06a
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• pp.64-73
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• 1995

The forging limit curves of sintered porous metals have been calculated, in terms of the two principal strains, by the Lee-Kuhn initial imperfection model. The various yield functions for porous metal have been applied to the initial imperfection model. When the value of initial imperfection ratio equals the value of initial relative density of the sintered porous metals, the calculation values are in good agreement with the measured data. The slopes of the forging limit curves are about 0.5 as in the case of non-porous metals.