• 한국안전학회지
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• 제19권4호
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• pp.155-160
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• 2004

판의 두께에 선형적으로 변화하는 온도분포의 열하중을 받는 단순지지의 사각형 박판을 해석하였다. 열에 의한 판의 처짐이 판두께에 비해 상대적으로 과대하여 막응력이 부수적으로 발생하여 문제는 비선형 해석이 된다. 큰 처짐을 가지는 기하학적 비선형 문제를 지배하는 기본방정식은 von Karman 방정식이 사용되며 차분법으로 수치해석 한다. 차분화 하여 얻어지는 유사선형 대수방정식은 반복법을 도입하여 해석하고 결과치를 해석적으로 얻은 해와 비교 검토한다.

• 대한기계학회논문집
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• 제19권8호
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• pp.1950-1963
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• 1995

A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

• Journal of Mechanical Science and Technology
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• 제20권11호
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• pp.1920-1933
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• 2006

Piezoelectric materials produce an electric field by deformation, and deform when subjected to an electric field. The coupling nature of piezoelectric materials has acquired wide applications in electric-mechanical and electric devices, including electric-mechanical actuators, sensors and structures. In this paper, a hollow sphere composed of a radially polarized spherically anisotropic piezoelectric material, e.g., PZT_5 or (Pb) (CoW) $TiO_3$ under internal or external uniform pressure and a constant potential difference between its inner and outer surfaces or combination of these loadings has been studied. Electrodes attached to the inner and outer surfaces of the sphere induce the potential difference. The governing equilibrium equations in radially polarized form are shown to reduce to a coupled system of second-order ordinary differential equations for the radial displacement and electric potential field. These differential equations are solved analytically for seven different sets of boundary conditions. The stress and the electric potential distributions in the sphere are discussed in detail for two piezoceramics, namely PZT _5 and (Pb) (CoW) $TiO_3$. It is shown that the hoop stresses in hollow sphere composed of these materials can be made virtually uniform across the thickness of the sphere by applying an appropriate set of boundary conditions.

• 대한토목학회논문집
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• 제26권5B호
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• pp.551-555
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• 2006

본 연구에서는 지진해일의 전파과정을 모의함에 있어 분산을 보다 정확하게 고려하기 위하여 선형 천수방정식을 leap-frog 기법으로 차분화한 후 분산보정항을 추가하여 실질적으로 선형 Boussinesq 방정식과 같은 정도로 분산효과를 고려할 수 있게 하였다. 기법의 정확성을 검증하기 위하여 Gauss 분포의 초기 수면변위를 갖는 문제에 적용하여 해석해와 비교하였고, 그 결과 본 연구에서 개발한 기법이 기존의 기법에 비해서 정확한 결과를 제공하였다.

• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.483-497
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• 2010

In this paper we study some qualitative behavior of the solutions of the difference equation $x_{n+1}=ax_n=\frac{bx_n}{cx_n-dx_{n-1}}$, n=0,1,$\ldots$, where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants with $cx_0-dx_{-1}\neq0$.

• Korean Journal of Mathematics
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• 제18권3호
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• pp.299-309
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• 2010

In this paper, we study the first order nonlinear neutral difference equation: $${\Delta}(x(n)+px(n-{\tau}))+f(n,x(n-c),x(n-d))=r(n),\;n{\geq}n_0$$. Using the Banach fixed point theorem, we prove the existence of bounded positive solutions of the equation, suggest Mann iterative schemes of bounded positive solutions, and discuss the error estimates between bounded positive solutions and sequences generated by Mann iterative schemes.

• East Asian mathematical journal
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• 제24권4호
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• pp.407-414
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• 2008

Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations with damping and convection terms, which describe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Journal of applied mathematics & informatics
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• 제6권1호
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• pp.15-30
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• 1999

In this paper the second order semi-discrete and full dis-crete generalized difference schemes for one dimensional parabolic equa-tions are constructed and the optimal order $H^1$ , $L^2$ error estimates and superconvergence results in TEX>$H^1$ are obtained. The results in this paper perfect the theory of generalized difference methods.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1247-1256
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• 2009

Finite difference schemes are considered for a nonlinear $Ca^{2+}$ diffusion equations with stationary and mobile buffers. The scheme inherits mass conservation as for the classical solution. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained. using the extended Lax-Richtmyer equivalence theorem.

• 대한수학회보
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• 제42권2호
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• pp.245-256
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• 2005

We consider the second-order nonlinear difference equation (1) $$\Delta(a_nh(x_{n+1}){\Delta}x_n)+p_{n+1}f(x_{n+1})=0,\;n{\geq}n_0$$ where ${a_n},\;{p_n}$ are sequences of integers with $a_n\;>\;0,\;\{P_n\}$ is a real sequence without any restriction on its sign. hand fare real-valued functions. We obtain some necessary conditions for (1) existing nonoscillatory solutions and sufficient conditions for (1) being oscillatory.