• Kyungpook Mathematical Journal
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• v.32 no.2
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• pp.159-166
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• 1992

• The Mathematical Education
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• v.23 no.1
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• pp.35-38
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• 1984

• Journal of the Korean Mathematical Society
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• v.20 no.2
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• pp.201-207
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• 1983

• The Mathematical Education
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• v.25 no.1
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• pp.33-37
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• 1986

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.113-122
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• 2005

We consider the iterative schemes for the large sparse linear system to solve partial differential equations. Using spectral radius of iteration matrices, the optimal relaxation parameters and good parameters can be obtained. With those parameters we compare the effectiveness of the SOR and SSOR algorithms. Applying Crank-Nicolson approximation, we observe the error distribution according to domain decomposition. The number of processors due to domain decomposition affects time and error. Numerical experiments show that effectiveness of SOR and SSOR can be reversed as time size varies, which is not the usual case. Finally, these phenomena suggest conjectures about equilibrium time grid for SOR and SSOR.

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

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.833-846
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• 1999

In this paper, we will study the relationship between the controlling factor of the solution to a difference equation and the solution of the corresponding differential equation. Many times the controlling factors are the same. But even the controlling factor of the two solutions may be different, we will discover a way to compute, for first order non-linear equations, the controlling factor of the solution to the difference equation using the solution of the differential equation.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1469-1484
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• 2014

In this paper we are concerned with a class of stochastic partial functional differential equations with infinite delay. Supposing that the linear part is a Hille-Yosida operator but not necessarily densely defined and employing the integrated semigroup and random dynamics theory, we present some appropriate conditions to guarantee the existence of a random attractor.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.245-257
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• 2008

In this paper, we find the sufficient conditions of controllability of semi-linear neutral functional differential evolution equations with non local conditions using by fractional power of operators and Sadovskii's fixed point theorem.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.989-993
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• 2001

This paper deals with the free vibrations of horizontally curved beams supported by non-homogeneous elastic foundation. Taking into account the effects of rotatory inertia and shear deformation, differential equations governing the free vibrations of such beams are derived, in which the linear elastic foundation is considered as the non-homogeneous foundation. Differential equations are solved numerically to calculate natural frequencies. In numerical examples, the parabolic curved member is considered. The parametric studies are conducted and the lowest four frequency parameters are reported in tables and figures as the non-dimensional forms.