• 한국방재학회:학술대회논문집
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• 한국방재학회 2007년도 정기총회 및 학술발표대회
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• pp.395-398
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• 2007

In this study, new dispersion-correction terms are added to leap-frog finite difference scheme for the linear shallow-water equations with the purpose of considering the dispersion effects of the linear Boussinesq equations for the propagation of tsunamis. The new model is applied to near Gadeok island in Pusan about The Central East Sea Tsunami in 1983 and The Hokkaldo Nansei Oki Earthquake Tsunami in 1993 one simulated in the study.

• 충청수학회지
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• 제20권4호
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• pp.449-455
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• 2007

We obtain a discrete version of a fundamental result by Yoshizawa related to the existence of almost periodic solutions of functional differential equations with finite delay.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.349-369
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• 2013

The present paper envisages the $q$-analogue of the exponential operators, determined by G. Dattoli and his collaborators for translation and diffusive operators which were utilized to establish analytical solutions of difference and integral equations. The generalization of their technique is expected to cover wide range of such utilization.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.181-203
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• 2018

In this paper, we have constructed an overlapping Schwarz method for singularly perturbed second order convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the central finite difference scheme on a uniform mesh while on the non-layer region we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. When appropriate subdomains are used, the numerical approximations generated from the method are shown to be first order convergent. Furthermore it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme is it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• 충청수학회지
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• 제24권4호
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• pp.639-663
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• 2011

Motivated by Agarwal and O'Regan ( Boundary value problems for general discrete systems on infinite intervals, Comput. Math. Appl. 33(1997)85-99), this article deals with the discrete type BVP of the infinite difference equations. The sufficient conditions to guarantee the existence of at least three positive solutions are established. An example is presented to illustrate the main results. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multi-fixed-point theorems can be extended to treat BVPs for infinite difference equations. The strong Caratheodory (S-Caratheodory) function is defined in this paper.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제13권2호
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• pp.171-180
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• 2009

This study investigates relationships between 7th and 8th grade students' achievements in forming and solving equations of. Study was conducted on randomly selected 7th and 8th grade students of elementary schools in Konya City, Turkey. 145 students (99 female, 46 male) participated in the research. Data were collected by an 'Equation Test'. The test which is suitable for equation types in 7th Grade Elementary Mathematics Curriculum. It was developed by the researchers. The relationships between achievements in forming and solving equations were examined by dependent samples t-test. The t-test results show that there is a significant difference. This difference is in the favor of equation solving (p>0.05). In other word, students are more successful in equation solving. In addition, students' achievements about different types of equations were investigated. The results show that the students have the highest achievement in ax=b type and the lowest achievement in (ax+b)/c=(dx+e)/f type of equations.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2006년도 학술발표회 논문집
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• pp.1935-1939
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• 2006

In this study, the new dispersion-correction terms are added to leap-frog finite difference scheme for the linear shallow-water equations with the purpose of considering the dispersion effects such as linear Boussinesq equations for the propagation of tsunamis. And, dispersion-correction factor is determined to mimic the frequency dispersion of the linear Boussinesq equations. The numerical model developed in this study is tested to the problem that initial free surface displacement is a Gaussian hump over a constant water depth, and the results from the numerical model are compared with analytical solutions. The results by present numerical model are accurate in comparison with the past models.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권3호
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• pp.157-175
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• 2019

In this paper we define higher-order Stieltjes derivatives, and using Schaefer's fixed point theorem we investigate the existence of solutions for a class of differential equations involving second-order Stieltjes derivatives with two-point boundary conditions. The equations include ordinary and impulsive differential equations, and difference equations.

• 충청수학회지
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• 제25권4호
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• pp.753-762
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• 2012

We study the BS-stability and the $\rho$-stability for functional difference equations with infinite delay as a discretization of Murakami and Yoshizawa's results [6] for functional differential equation with infinite delay.

• Kyungpook Mathematical Journal
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• 제60권2호
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• pp.401-413
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• 2020

In this article we consider the following system of piecewise linear difference equations: x_n+1 = |x_n| - y_n - 1 and y_n+1 = x_n + |y_n| - 1. We show that when the initial condition is an element of the closed second or fourth quadrant the solution to the system is either a prime period-3 solution or one of two prime period-4 solutions.