• Journal of the Korean Operations Research and Management Science Society
• /
• v.23 no.3
• /
• pp.27-36
• /
• 1998

This work has improved the method of Kim and Gal's (6) in that of requiring less response of the DM(decision maker) and ease of reply. The underlying notion is the MCDC(maximally changeable dominance cone) for describing all efficient solutions under the particular preference structure. According to the DM's partial preference expression, enlarging the MCDC is achieved, which results in reducing the solutions needed to take into consideration. The cone generators corresponding to the DM's response are added to the MCDC, which results the MCDC is enlarged. Adopting the scheme of pairwise comparison as a means of acquiring preference attitude, an improved interactive method is proposed. And also, a scheme of choosing a reference point is suggested to achieve the computational efficiency.

• Proceedings of the KIEE Conference
• /
• 1998.07a
• /
• pp.113-115
• /
• 1998

This paper presents the indirect boundary integral equation method(BIEM) to analyze 3D moving conductor problem. Instead of an artificial upwind algothm, the proposed method uses a fundamental Green's function which is a particular solution of diffusion equation. Therefore, this method yields a stable and accurate solution regardless of the Peclet number. The indirect BIEM is compared with 3D upwind FEM for a numerical model which has analytic solutions.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.1945-1962
• /
• 2015

This paper is mainly concerned with the formation of delta standing wave for the scalar conservation law with a linear flux function involving discontinuous coefficients by using the self-similar viscosity vanishing method. More precisely, we use the self-similar viscosity to smooth out the discontinuous coefficient such that the existence of approximate viscous solutions to the delta standing wave for the Riemann problem is established and then the convergence to the delta standing wave solution is also obtained when the viscosity parameter tends to zero. In addition, the Riemann problem is also solved with the standard method and the instability of Riemann solutions with respect to the specific small perturbation of initial data is pointed out in some particular situations.

• Structural Engineering and Mechanics
• /
• v.22 no.1
• /
• pp.107-130
• /
• 2006

The paper deals with the numerical solution of the dynamic problem of masonry structures. Masonry is modelled as a non-linear elastic material with zero tensile strength and infinite compressive strength. Due to the non-linearity of the adopted constitutive equation, the equations of the motion must be integrated directly. In particular, we apply the Newmark or the Hilber-Hughes-Taylor methods implemented in code NOSA to perform the time integration of the system of ordinary differential equations obtained from discretising the structure into finite elements. Moreover, with the aim of evaluating the effectiveness of these two methods, some dynamic problems, whose explicit solutions are known, have been solved numerically. Comparisons between the exact solutions and the corresponding approximate solutions obtained via the Newmark and Hilber-Hughes-Taylor methods show that in the cases under consideration both numerical methods yield satisfactory results.

• East Asian mathematical journal
• /
• v.40 no.3
• /
• pp.295-306
• /
• 2024

We investigate the existence of multiple positive solutions of the following elliptic equation with a Schrödinger-type term: $$\begin{cases}-{\Delta}u+V(x)u={\lambda}f(u){\quad} x{\in}{\Omega},\\{\qquad}{\qquad}{\quad}u=0, {\qquad}\;x{\in}\partial{\Omega},\end{cases}$$, where 0 ∈ Ω is a bounded domain in ℝ^N , N ≥ 1, with a smooth boundary ∂Ω, f ∈ C[0, ∞), V ∈ L^∞(Ω) and λ is a positive parameter. In particular, when f(s) > 0 for 0 ≤ s < σ and f(s) < 0 for s > σ, we establish the existence of at least three positive solutions for a certain range of λ by using the method of sub and supersolutions.

• Coupled systems mechanics
• /
• v.10 no.1
• /
• pp.79-102
• /
• 2021

In this paper we deal with instability problems of structures under nonconservative loading. It is shown that such class of problems should be analyzed in dynamics framework. Next to analytic solutions, provided for several simple problems, we show how to obtain the numerical solutions to more complex problems in efficient manner by using the finite element method. In particular, the numerical solution is obtained by using a modified Euler-Bernoulli beam finite element that includes the von Karman (virtual) strain in order to capture linearized instabilities (or Euler buckling). We next generalize the numerical solution to instability problems that include shear deformation by using the Timoshenko beam finite element. The proposed numerical beam models are validated against the corresponding analytic solutions.

• East Asian mathematical journal
• /
• v.39 no.3
• /
• pp.355-367
• /
• 2023

Extending [14], we establish the existence of multiple positive solutions for a Schrödinger-type singular elliptic equation: $$\{{-{\Delta}u+V(x)u={\lambda}{\frac{f(u)}{u^{\beta}}},\;x{\in}{\Omega}, \atop u=0,\;x{\in}{\partial}{\Omega},$$ where 0 ∈ Ω is a bounded domain in ℝ^N, N ≥ 1, with a smooth boundary ∂Ω, β ∈ [0, 1), f ∈ C[0, ∞), V : Ω → ℝ is a bounded function and λ is a positive parameter. In particular, when f(s) > 0 on [0, σ) and f(s) < 0 for s > σ, we establish the existence of at least three positive solutions for a certain range of λ by using the method of sub and supersolutions.

• Honam Mathematical Journal
• /
• v.30 no.4
• /
• pp.631-635
• /
• 2008

In this paper we discuss on the formal linearization and exact solution of Klein-Gordon's equation (1) $u_{tt}-au_{xx}+bu-cu^3=0 a,b,c{\in}R^+$ So that we know an efficient method for constructing of particular solutions of some nonlinear partial differential equations is introduced.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.3
• /
• pp.497-512
• /
• 2021

In this paper, we study the analytical and approximate solutions for a fractional quadratic integral equation involving Katugampola fractional integral operator. The existence and uniqueness results obtained in the given arrangement are not only new but also yield some new particular results corresponding to special values of the parameters 𝜌 and ϑ. The main results are obtained by using Banach fixed point theorem, Picard Method, and Adomian decomposition method. An illustrative example is given to justify the main results.

• Journal of the Korean earth science society
• /
• v.39 no.5
• /
• pp.473-482
• /
• 2018

During the period of 2002 to 2017, the Gravity Recovery And Climate Experiment (GRACE) had observed time-varying gravity changes with unprecedented accuracy. The GRACE science data centers provide the monthly gravity solutions after removing the sub-monthly mass fluctuation using geophysical models. However, model misfit makes the solutions to be contaminated by aliasing errors, which exhibits peculiar north-south stripes. Two conventional filters are used to reduce the errors, but signals with similar spatial patterns to the errors are also removed during the filtering procedure. This would be particularly problematic for estimating the ice mass changes in Western Antarctic Ice Sheet (WAIS) and Antarctic Peninsula (AP) due to their similar spatial pattern to the elongated north-south direction. In this study, we introduce an alternative filter to remove aliasing errors using the Empirical Orthogonal Functions (EOF) analysis. EOF can decompose data into different modes, and thus is useful to separate signals from noise. Therefore, the aliasing errors are effectively suppressed through EOF method. In particular, the month-to-month mass changes in WAIS and AP, which have been significantly contaminated by aliasing errors, can be recovered using EOF method.