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

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

• The Mathematical Education
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• v.21 no.1
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• pp.25-28
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• 1982

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.57-72
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• 2008

This paper is concerned with the numerical solutions to steady state nonlinear elliptical partial differential equations (PDE) of the form $u_{xx}+u_{yy}+Du_{x}+Eu_{y}+Fu=G$, where D, E, F are functions of x, y, u, $u_{x}$, and $u_{y}$, and G is a function of x and y. Dirichlet boundary conditions in a rectangular region are considered. We propose alternating direction shooting method for solving such nonlinear PDE. Numerical results show that the alternating direction shooting method performed better than the commonly used linearized iterative method.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.156-162
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• 1998

The main objective of this paper is to study the boundedness of solutions of the differential equation $L_{n} {\chi}＋F(t,{\chi}) = f(t), n {\geq} 2 $(*) Necessary and sufficient conditions for boundedness of all solutions of (*) will be obtainded. The asymptotic behavior of solutions of (*) will also be studied.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.217-221
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• 2005

This paper we consider the solution of differential equations with fuzzy coefficients generated by fuzzy number $\~{1}$ using two different methods with eigenvalues and eigenvectors.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1725-1739
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• 2016

Abstract. Numerical solutions for the evolutionary space fractional order differential equations are considered. A predictor corrector method is applied in order to obtain numerical solutions for the equation without solving nonlinear systems iteratively at every time step. Theoretical error estimates are performed and computational results are given to show the theoretical results.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.499-511
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• 2015

This paper shows that the solutions to the perturbed dierential system $$y^{\prime}=f(t,y)+{\int}_{t_o}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded property. To show this property, we impose conditions on the perturbed part ${\int}^{t}_{t_o}g(s,y(s))ds+h(t,y(t),Ty(t))$ and on the fundamental matrix of the unperturbed system y' = f(t, y).

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.763-769
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• 2014

In this paper, we illustrate a counter example for the converse of a certain conjecture proposed by De Giorgi. De Giorgi suggested a series of conjectures, in which a certain integral condition for singularity or degeneracy of an elliptic operator is satisfied, the solutions are continuous. We construct some singular elliptic operators and solutions such that the integral condition does not hold, but the solutions are continuous.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.83-94
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• 1996

Classical mechanics begins with some variants of Newton's laws. Lagrangian mechanics describes motion of a mechanical system in the configuration space which is a differential manifold defined by holonomic constraints. For a conservative system, the equations of motion are derived from the Lagrangian function on Hamilton's variational principle as a system of the second order differential equations. Thus, for conservative systems, Newtonian mechanics is a particular case of Lagrangian mechanics.(omitted)