• Journal of KSNVE
• /
• v.7 no.3
• /
• pp.489-498
• /
• 1997

In this paper, chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonliear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which has the external and parametric excitation with a same frequency. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Numerical simulations are performed to demonstrate theoretical results and show the strange attractor of the chaotic motion.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.297-310
• /
• 2018

In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}-norm$. Some numerical examples are given in order to validate the theoretical results.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.317-329
• /
• 2006

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

• 전기의세계
• /
• v.21 no.4
• /
• pp.7-14
• /
• 1972

The author has established a general equation for the travelling magnetic field in air gap with the end effect taken into consideration, which constitutes the basics for the analysis of characteristics of linear induction motor. This equation is verified by comparison of the experimental values with the theoretically calculated values. The properties of the travelling wave with attenuation, which is contained in the travelling magnetic field of linear induction motor, have been verified, and consequently the practicable equation is established with these effects taken into consideration. This provides the solid foundation for the theoretical analysis of the characteristics of the linear induction motor.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.43-55
• /
• 2007

In this paper, an $H^1-Galerkin$ mixed finite element method is used to approximate the solution as well as the flux of Burgers' equation. Error estimates have been derived. The results of the numerical experiment show the efficacy of the mixed method and justifies the theoretical results obtained in the paper.

• 전기의세계
• /
• v.16 no.1
• /
• pp.14-18
• /
• 1967

To analyze th frequency modulation system the characteristic equation of the F-M system, i.e., Mathieu's equation, is derived from the equivalent circuits of direct modulation system. The analysis of F-M equation is undertaken by the Yonsei 101 Analog Computer. And the computer solution is compared with the theoretical solution. It is concluded that not only the frequency but also the amplitude of the carrier wave are changed by varying the modulation index and the system becomes unstable if the modulation index is increased near to unity.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1996.10a
• /
• pp.288-294
• /
• 1996

In this paper, Chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonlinear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which have the parametric and external excitation. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Poincare maps numerically demonstrate theoretical results and show transverse homoclinic orbit of the chaotic motion.

• Journal of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.279-298
• /
• 2022

In this paper, the existence and uniqueness for the global solution of neutral stochastic functional differential equation is investigated under the locally Lipschitz condition and the contractive condition. The implicit iterative methodology and the Lyapunov-Razumikhin theorem are used. The stability analysis for such equations is also applied. One numerical example is provided to illustrate the effectiveness of the theoretical results obtained.

• Journal of Environmental Science International
• /
• v.11 no.9
• /
• pp.907-914
• /
• 2002

Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.

• Journal of the Korean Applied Science and Technology
• /
• v.23 no.3
• /
• pp.185-191
• /
• 2006

It is desirable to have an accurate expression on the temperature dependence of surface(or interfacial) tension ${\sigma}$, because most of the interfacial thermodynamic functions can be derived from it. There have been proposed several equations on the temperature dependence of the surface tension, ${\sigma}(T)$. Among them $E{\ddot{o}}tv{\ddot{o}}s$ equation and the one modified by Katayama, which is called Katayama equation, for improving accuracies of $E{\ddot{o}}tv{\ddot{o}}s$ equation close to critical points, have been most well-known. In this article Katayama equation is interpreted on the basis of the cell model to understand the nature of the equation. The cell model results in an expression very similar to Katayama equation. This implies that, although $E{\ddot{o}}tv{\ddot{o}}s$ and Katayama equations were obtained on the basis of experimental results, they have a sound theoretical background. The Katayama equation is also modified with the phase volume replaced with a critical scaling expression. The modified Katayama equation becomes a power-law equation with the exponent slightly different from the value obtained by critical-scaling theory. This implies that Katayama equation can be replaced by a critical-scaling equation which is proven to be accurate.