• KSCE Journal of Civil and Environmental Engineering Research
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• v.5 no.3
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• pp.31-38
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• 1985

The governing differential equations and the boundary conditions for the free vibration of fixed-ended uniform parabolic arch are derived on the basis of the equilibrium equations and the D'Alembert principle. The effect of rotary inertia as well as extensional and flexural deformations is considered in the governing differential equations. A trial elgenvalue method is used for determining the natural frequencies. The Runge-Kutta method is used in this method to perform the integration of the differential equations. The detailed studies are made of the lowest three vibration frequencies for the span length equal to 10m. The effect of the rotary inertia is analyzed and it's numerical data are presented in table. And as the numerical results the frequency versus the rise of arch and the radius of gyration are presented in figures.

• Journal of Astronomy and Space Sciences
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• v.14 no.1
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• pp.136-141
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• 1997

To calculate the position and velocity of the artificial satellite precisely, one has to build a mathematical model concerning the perturbations by understanding and analysing the space environment correctly and then quantifying. Due to these space environment model, the total acceleration of the artificial satellite can be expressed as the 2nd order differential equation and we build an orbit propagation algorithm by integrating twice this equation by using the Cowell's method which gives the position and velocity of the artificial satellite at any given time. Perturbations important for the orbits of geostationary spacecraft are the Earth's gravitational potential, the gravitational influences of the sun and moon, and the solar radiation pressure. For precise orbit propagation in Cowell' method, 40 x 40 spherical harmonic coefficients can be applied and the JPL DE403 ephemeris files were used to generate the range from earth to sun and moon and 8th order Runge-Kutta single step method with variable step-size control is used to integrate the the orbit propagation equations.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.6
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• pp.73-79
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• 2009

For the shake of control for movement object, control theory like neural network, nonlinear model predictive control(NMPC) is realized on digital high speed computer. Predictor of flight control system(FCS) based nonlinear model predictive control has to be satisfied with response for hard real-time to perform applications on each module in the FCS. Simultaneously, It gives a serious consideration accuracy to give full play to FCS's performance. Error of mathematical aspect affects realization of whole algorithm. But factors of bring mathematical error is not considered to calculate final accuracy on parameter of predictor. In this paper, Predictor was made using load control model on the digital computer for design FCS at hard real-time and is shown response time on realization algorithm. And is shown realization algorithm of high effective predictor over the accuracy. The predictor was realized on the load control model using Euler method, Heun method, Runge-Kutta and Taylor method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.185-223
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• 2022

The classical equation of Jonathan Homer Lane and Robert Emden, a nonlinear second-order ordinary differential equation, models the isothermal spherical clouded gases under the influence of the mutual attractive interaction between the gases' molecules. In this paper, the Adomian decomposition method (ADM) is presented to obtain highly accurate and reliable analytical solutions of a class of generalised Lane-Emden equations with strong nonlinearities. The nonlinear term f(y(x)) of the proposed problem is given by the integer powers of a continuous real-valued function h(y(x)), that is, f(y(x)) = h^m(y(x)), for integer m ≥ 0, real x > 0. In the end, numerical comparisons are presented between the analytical results obtained using the ADM and numerical solutions using the eighth-order nested second derivative two-step Runge-Kutta method (NSDTSRKM) to illustrate the reliability, accuracy, effectiveness and convenience of the proposed methods. The special cases h(y) = sin y(x), cos y(x); h(y) = sinh y(x), cosh y(x) are considered explicitly using both methods. Interestingly, in each of these methods, a unified result is presented for an integer power of any continuous real-valued function - compared with the case by case computations for the nonlinear functions f(y). The results presented in this paper are a generalisation of several published results. Several examples are given to illustrate the proposed methods. Tables of expansion coefficients of the series solutions of some special Lane-Emden type equations are presented. Comparisons of the two results indicate that both methods are reliably and accurately efficient in solving a class of singular strongly nonlinear ordinary differential equations.

• Journal of Advanced Marine Engineering and Technology
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• v.24 no.1
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• pp.25-30
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• 2000

In present paper, mass transfer over a flat plate with film condensation including noncondesable gas is analyzed with the help of similarity methods. Couette flow was assumed in liquid film and boundary-layer approximation was used in the ambient flow. Governing equations were transformed into the ordinary differential equtions by the similarity methods. Runge-Kutta and shooting method were used in order to fine the effect of mass transfer on the velocity and concentrations at the liquid-vapor interface.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.613-625
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• 2001

In this paper, we investigate a simplified model of a particle suspended elastically from two towers by two nonlinear elastic springs, with a restoring force similar to Hooke’s law under extension and with no resistance to compression. Numerical results are presented, showing the solutions can be either of the same period oscillation the forcing term, can be a subharmonic response of multiple period, or can be noisy periodic which is apparently chaotic. Multiplicity of periodic solutions for certain physical parameters are demonstrated.

• 한국가스학회:학술대회논문집
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• 1997.09a
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• pp.14-19
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• 1997

A numerical method for determining the temperature vartiation in a natural gas transmission line is presented. By considering an element of the gas pipeline and assuming radially lumped heat transfer at steady-state conditions, the energy equation is developed. The integration of the developed nonlinear differential equation is done numerically using the fourth order Runge-Kutta scheme. The results of the present study have been compared with the results of Coulter equations, and show a fairly good agreement.

• Journal of the Korean Society of Marine Environment & Safety
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• v.1 no.1
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• pp.27-38
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• 1995

In this paper, a program for the calculation of GZ curve for a ship in waves is developed and GZ curves for a ferry in the still water and in waves are calculated. And the added mass, damping, restoring forces and wave exciting forces are calculated by using the strip theory given by Salvesen, Tuck, Faltinsen. Capsizing simulations are perfoned in consideration if the nonlinear restoring forces of the ship in waves by using the Runge-Kutta 4-th method.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1997.04a
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• pp.204-209
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• 1997

This paper reports on the theoretical study of the vane motions in a positive displacement vane pump. Vane detachment cause the pressure fluctuation, noise, wear in cam ring, and decrease the volumetric efficiency. Dynamic equation of vane motion and flow continuity equation have been modeled and solved simultaneously using 4th order Runge-Kutta method. As results of analysis, vane detachment occurs due to pressure overshoot by excess compression in the pumping chamber. Amount of vane detachment has been reduced by decreasing the pressure overshoot.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.5
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• pp.516-518
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• 1990

We have derived the equation which involves the variation of electron energy with time in a lowly ionized plasma when a low alternating electric field is applied. We consider only elastic collisions between electrons and neutral atoms. This equation is solved using the 4th-order Runge-Kutta method, and applied to argon gas discharge which is driven by source frequency of 100, 1K, 10K, 100K, and 1M (Hz). The results show that the variation of electron energy becomes flat with higher frequencies.