• 한국수학교육학회지시리즈E:수학교육논문집
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• 제28권3호
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• pp.339-352
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• 2014

본 연구에서는 2009 개정 교육과정에 따른 수학과 교육과정에서 도입한 미분방정식 지도를 위한 수학적 모델링을 소개한다. 2014년에 1개 출판사만으로 출간된 '고급수학 II'의 교과서는 이계미분방정식 y"+y=0의 풀이를 거듭제곱 급수 방법을 사용하고 있다. 이에 따른 문제점을 알아보고 그 대안을 제시한다. 또한, 고급수학 II 교과서는 기계적 시스템을 다루고 있지만 전기적 시스템은 다루지 않고 있다. 따라서 교과서에서 다루는 일 계미분방정식을 전기회로로 지도하는 방안을 제시한다. 끝으로 미분방정식 지도와 관련된 용어를 제시한다.

• 대한전기학회논문지:시스템및제어부문D
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• 제55권1호
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• pp.17-19
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• 2006

This paper presents the design of an electromagnetic system such as jumping ring system, and also considers the characteristics of dynamics for system with initial parameter. For the propose of system analysis, the MATLAB tool is to solve coupled differential equations with inductances and mutual inductance. To apply a real electromagnetic system, this paper implements the jumping ring system using design parameters, and analyzes the jumping ring system with proposal step.

• 대한수학회지
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• 제42권2호
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• pp.269-289
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• 2005

An infinite system of stochastic differential equations (SDE)driven by Brownian motions and compensated Poisson random measures for the locations and weights of a collection of particles is considered. This is an analogue of the work by Kurtz and Xiong where compensated Poisson random measures are replaced by white noise. The particles interact through their weighted measure V, which is shown to be a solution of a stochastic differential equation. Also a limit theorem for system of SDE is proved when the corresponding Poisson random measures in SDE converge to white noise.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권3호
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• pp.201-215
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• 2018

In this paper we consider a class of singularly perturbed system of delay differential equations of convection diffusion type with integral boundary conditions. A finite difference scheme on an appropriate piecewise Shishkin type mesh is suggested to solve the problem. We prove that the method is of almost first order convergent. An error estimate is derived in the discrete maximum norm. Numerical experiments support our theoretical results.

• 대한수학회논문집
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• 제38권1호
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• pp.281-298
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• 2023

A class of systems of Caputo fractional differential equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a uniform mesh is proposed. Supremum norm is used to derive an error estimate which is of order κ − 1, 1 < κ < 2. Numerical examples are given which validate our theoretical results.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.449-471
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• 2023

In this paper, we study a linear system of homogeneous commensurate /incommensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.

• 대한수학회보
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• 제52권6호
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• pp.1973-2000
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• 2015

In this study, we present a multidimensional open system for valveless pumping (VP). This system consists of an elastic tube connected to two open tanks filled with a fluid under gravity. The two-dimensional elastic tube model is constructed based on the immersed boundary method, and the tank model is governed by a system of ordinary differential equations based on the work-energy principle. The flows into and out of the elastic tube are modeled in terms of the source/sink patches inside the tube. The fluid dynamics of this system is generated by the periodic compress-and-release action applied to an asymmetric region of the elastic tube. We have developed an algorithm to couple these partial differential equations and ordinary differential equations using the pressure-flow relationship and the linearity of the discretized Navier-Stokes equations. We have observed the most important feature of VP, namely, the existence of a unidirectional net flow in the system. Our computations are focused on the factors that strongly influence the occurrence of unidirectional flows, for example, the frequency, compression duration, and location of pumping. Based on these investigations, some case studies are performed to observe the details of the ow features.

• 대한수학회지
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• 제56권1호
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• pp.127-147
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• 2019

In this paper we establish some new explicit solutions for impulsive linear fractional differential equations with impulses at fixed times, which provides a handy tool in deriving singular integral-sum inequalities and an impulsive fractional comparison principle. Thus we study the Mittag-Leffler stability of impulsive differential equations with the Caputo fractional derivative by using the impulsive fractional comparison principle and piecewise continuous functions of Lyapunov's method. Also, we give some examples to illustrate our results.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2005년도 추계학술대회 논문집
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• pp.1165-1170
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• 2005

In order to perform the spatial buckling analysis of the curved beam element with nonsymmetric thin-walled cross section, exact static stiffness matrices are evaluated using equilibrium equations and force-deformation relations. Contrary to evaluation procedures of dynamic stiffness matrices, 14 displacement parameters are introduced when transforming the four order simultaneous differential equations to the first order differential equations and 2 displacement parameters among these displacements are integrated in advance. Thus non-homogeneous simultaneous differential equations are obtained with respect to the remaining 8 displacement parameters. For general solution of these equations, the method of undetermined parameters is applied and a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices are solved with respect to 12 displacement parameters. Resultantly displacement functions are exactly derived and exact static stiffness matrices are determined using member force-displacement relations. The buckling loads are evaluated and compared with analytic solutions or results by ABAQUS's shell element.

• 대한수학회지
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• 제53권5호
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• pp.1019-1036
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• 2016

In this paper, we study the existence of solutions and $L^2$-regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the non-linear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.