• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.319-330
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• 2002

The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green\`s function is constructed. Fer nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.419-430
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• 2016

In this paper, we investigate the existence and uniqueness of positive solutions for three-point boundary value problem of nonlinear fractional q-difference equation. Some existence and uniqueness results are obtained by applying some standard fixed point theorems. As applications, two examples are presented to illustrate the main results.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.101-110
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• 2006

In this paper, we develop existence and uniqueness criteria to certain class of three point boundary value problems associated with third order nonlinear fuzzy differential equations, with the help of Green's functions and contraction mapping principle.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.11
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• pp.505-513
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• 2001

This paper presents the new three-level optimal control scheme for the large scale nonlinear systems, which is based on fast walsh transform. It is well known that optimization for nonlinear systems leads to the resolution of a nonlinear two point boundary value problem which always requires a numerical iterative technique for their solution. However, Three-level costate coordination can avoid two point boundary condition in subsystem. But this method also has the defect that must solve high order differential equation in intermediate level. The proposed method makes use of fast walsh transform, therefore, is simple in computation because of solving algebra equation instead of differential equation.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.683-686
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• 2002

The hydrodynamic instability of the three-dimensional boundary-layer over a rotating disk has been numerically investigated for three cases flows using linear stability theory (i.e. Rossby number, Ro = -1, 0, and 1). Detailed numerical values of the disturbance wave number, wave frequency, azimuth angle, radius (Reynolds number, Re) and other characteristics have been calculated for $K{\acute{a}}rm{\acute{a}}n$, Ekman and $B{\"{o}}ewadt$ boundary-layer flows. Neutral curves for these flows are presented. Presented are the neutral stability results concerning the two instability modes (Type I and Type II) by using a two-point boundary value problem code COLUEW that was based upon the adaptive orthogonal collocation method using B-spline. The prediction from the present results on both instability modes among the three cases agrees with the previously known numerical and experimental data well.

• Computers and Concrete
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• v.23 no.3
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• pp.171-188
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• 2019

This study proposed a new and efficient 2D damage-plasticity model within the framework of Isogeometric analysis (IGA) for the geometrically nonlinear damage analysis of concrete. Since concrete exhibits complicated material properties, two internal variables are introduced to measure the hardening/softening behavior of concrete in tension and compression, and an implicit gradient-enhanced formulation is adopted to restore the well-posedness of the boundary value problem. The numerical results calculated by the model is compared with the experimental data of three benchmark problems of plain concrete (three-point and four-point bending single-notched beams and four-point bending double-notched beam) to illustrate the geometrical flexibility, accuracy, and robustness of the proposed approach. In addition, the influence of the characteristic length on the numerical results of each problem is investigated.

• Structural Engineering and Mechanics
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• v.27 no.5
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• pp.609-623
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• 2007

The problem of a semi-infinite magneto-electro-elastically impermeable mode-III crack in a magneto-electro-elastic material is considered under the action of impact loads. For the case when a pair of concentrated anti-plane shear impacts, electric displacement and magnetic induction impacts are exerted symmetrically on the upper and lower surfaces of the crack, the magneto-electro-elastic field ahead of the crack tip is determined in explicit form. The dynamic intensity factors and dynamic energy density factor are obtained. The method adopted is to reduce the mixed initial-boundary value problem, by using the Laplace and Fourier transforms, into three simultaneous dual integral equations, one of which is converted into an Abel's integral equation and the others into a singular integral equation with Cauchy kernel. Based on the obtained fundamental solutions of point impact loads, the solutions of two kinds of different loading cases are evaluated by integration. For some particular cases, the present results reduce to the previous results.

• School Mathematics
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• v.17 no.2
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• pp.241-255
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• 2015

The purpose of this study is to analyze teachers' understanding on generating random number in Monte Carlo simulation and to provide educational implications in school practice. The results showed that the 70% of the teachers selected wrong ideas from three types for random-number as strategies for problem solving a probability problem and also they make some errors to justify their opinion. The first kind of the errors was that the probability of a point or boundary was equal to the value of the probability density function in the continuous probability distribution. The second kind of the errors was that the teachers failed to recognize that the sample space has been changed by conditional probability. The third kind of the errors was that when two random variables X, Y are independence of each other, then only, joint probability distribution is satisfied $P(X=x,\;Y=y)=p(X=x){\times}P(Y=y{\mid}X=x)$.