• 대한수학회논문집
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• 제33권4호
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• pp.1217-1227
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• 2018

In the paper, we study the growth and fixed point of solutions of high order linear differential equations with entire coefficients of [p, q]-order in the complex plane. We improve and extend some results due to T. B. Cao, J. F. Xu, Z. X. Chen, and J. Liu, J. Tu, L. Z. Shi.

• Water Engineering Research
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• 제1권4호
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• pp.293-298
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• 2000

Optimal values of $\alpha$ characterizing the linear dispersion property in the modified Boussinesq equations are determined by minimizing the combined relative errors of the phase and group velocities. The value of $\alpha$ is fixed in previous studies, whereas it is varying in the present study. The phase and group velocities are calculated by using variable $\alpha$ and compared to those of the linear Stokes wave theory and previous studies. It is found that the present study produces the best match to the linear Stokes theory.

• 충청수학회지
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• 제29권3호
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• pp.515-521
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• 2016

This paper deals with linear impulsive differential equations with non-integer orders. We provide the explicit representation of solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions.

• Kyungpook Mathematical Journal
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• 제53권4호
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• pp.553-563
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• 2013

We derive a family of non-linear differential equations from the generating functions of the Euler polynomials and study the solutions of these differential equations. Then we give some new and interesting identities and formulas for the Euler polynomials of higher order by using our non-linear differential equations.

• Kyungpook Mathematical Journal
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• 제48권1호
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• pp.123-132
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• 2008

In this paper, we investigate higher-order linear differential equations with entire coefficients of iterated order. We improve and extend the result of L. Z. Yang by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen and the extended Wiman-Valiron theory by Wang and Yi. We also consider the nonhomogeneous linear differential equations.

• 대한수학회논문집
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• 제34권4호
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• pp.1245-1259
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• 2019

In the paper, we study the growth properties of meromorphic solutions of higher order linear differential equations with entire coefficients of [p, q] - ${\varphi}$ order, ${\varphi}$ being a non-decreasing unbounded function and establish some new results which are improvement and extension of some previous results due to Hamani-Belaidi, He-Zheng-Hu and others.

• Journal of Advanced Marine Engineering and Technology
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• 제15권4호
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• pp.46-53
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• 1991

In the present study, Navier-Stokes equation is numerically solved by use of a Finite analytic method to obtain the 2-dimensional flow field in the square cavity. The basic idea of F.A.M. is the incorporation of local analytic solutions in the numerical solution of linear or non-linear partial differential equations. In the F.A.M., the total problem is subdivided into a number of all elements. The local analytic solution is obtained for the small element in which the governing equation, if non-linear, to be linearized. The local analytic solutions are then expressed in algebraic form and are overlapped to cover the entire region of the problem. The assembly of these local analytic solutions, which still preserve the overall nonlinearity of the governing equations, results in a system of linear algebraic equations. The system of algebraic equations is then solved to provide the numerical solutions of the total problem. The computed flow field shows the same characteristics to physical concept of flow phenomena.

• 대한수학회지
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• 제46권4호
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• pp.747-758
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• 2009

In this paper, we investigate the growth and fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives. Because of the restriction of differential equations, we obtain that the properties of fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives are more interesting than that of general transcendental meromorphic functions. Our results extend the previous results due to M. Frei, M. Ozawa, G. Gundersen, and J. K. Langley and Z. Chen and K. Shon.

• 한국정밀공학회지
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• 제12권6호
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• pp.145-151
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• 1995

The first-order Taylor series expansion can be evaluated analytically from the formulated symbolic nonlinear dynamic equations. A closed-form linear dynamic euation is derived about a nominal trajectory. The state space representation of the linearized dynamics can be derived easily from the closed-form linear dynamic equations. But manual symbolic expansion of dynamic equations and linearization is tedious, time-consuming and error-prone. So it is desirable to manipulate the procedures using a computer. In this paper, the analytic linearization is performed using the symbolic language MATHEMATICA. Two examples are given to illustrate the approach anbd to compare nonlinear model with linear model.

• 충청수학회지
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• 제21권3호
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• pp.395-401
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• 2008

In this paper we investigate h-stability for linear dynamic equations on time scales under $u_{\infty}$-similarity.