• 대한수학회지
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• 제45권1호
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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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• 제26권4호
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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 applied mathematics & informatics
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• 제23권1_2호
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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.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.331-348
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• 2018

In this paper, an initial value method for solving a class of singularly perturbed delay differential equations with layer behavior is proposed. In this approach, first the given problem is modified in to an equivalent singularly perturbed problem by approximating the term containing the delay using Taylor series expansion. Then from the modified problem, two explicit Initial Value Problems which are independent of the perturbation parameter, ${\varepsilon}$, are produced: the reduced problem and boundary layer correction problem. Finally, these problems are solved analytically and combined to give an approximate asymptotic solution to the original problem. To demonstrate the efficiency and applicability of the proposed method three linear and one nonlinear test problems are considered. The effect of the delay on the layer behavior of the solution is also examined. It is observed that for very small ${\varepsilon}$ the present method approximates the exact solution very well.

• 충청수학회지
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• 제35권1호
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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.

• 한국융합학회논문지
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• 제12권5호
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• pp.303-311
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• 2021

본 연구에서는 한국복지패널(Korean Welfare Panal Study) 11차년도(2016년), 12차년도(2017년), 13차년도(2018년), 14차년도(2019년) 자료 중 가구주용 데이터와 가구원용 데이터를 활용하여 성인의 문제음주가 우울에 종단적 영향을 미치는지에 대해 검증하였다. 분석결과, 첫째, 우울의 초기값은 문제음주 초기값과 정적(+)인 관계가 있는 것으로 나타났고, 문제음주 변화율과도 유의미한 관계가 나타났다. 둘째, 수급가구의 경우는 우울의 초기값, 문제음주의 초기값과 정적(+)인 관계를 나타냈다. 셋째, 장애인의 경우는 우울의 초기값, 문제음주 초기값과 부적(-)인 관계를 나타냈다. 따라서 성인기 이전의 학교교육에서 음주문제 예방 프로그램 개발과 교육이 적극적으로 이루어져야 할 것을 제언하였다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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• pp.372-376
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• 1989

One of the major difficulties with modular approach model of separation process simulation is initial guess problem. Only accurate initial guess make the problem converge and large computer memory and calculating time are required. In this study, we use the initial bottom guess value same as given feed condition and update the value the .theta.method. So we examine;(1)the problem converges using initial guess with large range, (2)computer memory and calculating time are reduced considerably.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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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 Society for Industrial and Applied Mathematics
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• 제3권1호
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• pp.1-15
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• 1999

Gradient recovery techniques for the second order elliptic boundary value problem are well known. In particular, the Midpoint and the Vertex Recovery Operator have been studied by various authors and under suitable assumptions on the regularity of the unknown solution superconvergence property of these recovered gradients have been proved. In this paper we extend these results to the recovered gradient of the finite element approximation to a model initial-boundary value problem, and go on to prove superconvergence result for this recovered gradient in a discrete (in time) error norm.

• 충청수학회지
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• 제29권2호
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• pp.337-346
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• 2016

Within white noise approach, we study the existence and uniqueness of the solution of an initial value problem for generalized white noise functionals, and then as a corollary we discuss the linear stochastic differential equation associated with a convolution of white noise functionals.