• Journal of Korea Water Resources Association
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• v.39 no.7 s.168
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• pp.593-603
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• 2006

The basin response to storm is regarded as nonlinearity inherently. In addition, the consistent nonlinearity of hydrologic system response to rainfall has been very tough and cumbersome to be treated analytically. The thing is that such nonlinear models have been avoided because of computational difficulties in identifying the model parameters from recorded data. The parameters of nonlinear system considered as dynamic effects in the conceptual model are optimized as the sum of errors between the observed and computed runoff is minimized. For obtaining the optimal parameters of functions, the historical data for the Bocheong watershed in the Geum river basin were tested by applying the numerical methods, such as quasi-linearization technique, Runge-Kutta procedure, and pattern-search method. The estimated runoff carried through from the storage function with dynamic effects was compared with the one of 1st-order differential equation model expressing just nonlinearity, and also done with Nash model. It was found that the 2nd-order model yields a better prediction of the hydrograph from each storm than the 1st-order model. However, the 2nd-order model was shown to be equivalent to Nash model when it comes to results. As a result, the parameters of nonlinear 2nd-order differential equation model performed from the present study provided not only a considerable physical meaning but also a applicability to Korean watersheds.

• Water for future
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• v.29 no.5
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• pp.173-184
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• 1996

In this study, a two-dimensional shallow-water equation was used to develop the mathematical model for computing water levels and flow distribution. In the discretization equations, based on the finite volume method (FVM), the third order Runge-Kutta method and the third order upwind scheme were introduced to handle the unsteady and vconvective terms in the governing equations. To determine the accuracy of the developed model, it was applied to the rectangular horizontal channel in a frictionless flow. The water depth and velocity obtained by the numerical model were found to agree closely with the exact solution. The model was also applied to the rectangular channel with both the symmetric and the non symmetric constriction. The velocity distribution of the flow and the propagation of the flood wave were simulated and the results well described the flow characteristics.

• Journal of Biomedical Engineering Research
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• v.24 no.4
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• pp.347-354
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• 2003

In this paper, a computational method of an action potential including the effect of extremely low frequency and mobile phone (external) electromagnetic fields is Proposed. The method is based on the Hodgkin and Huxley model, applies the effect of the electromagnetic fields on the action Potential in terms of a binding factor into the injection current of the model, and calculates the Strength-Duration curve from numerical experiments for a frequency range of electromagnetic fields. In the numerical experiments, the coupled ordinary differential equations of the action potential and the state variables are solved solf-consistently by using Runge-Kutta Fehlberg method. The range of the frequency considered is from 1Hz through 100Hz and of 900MHz, which is specific for a mobile Phone. The Strength-Duration curves resulted showed good agreements with the equation suggested by Hodgkin and Huxley.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.601-621
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• 2019

This study presents a comprehensive nonlinear dynamic approach to investigate the linear and nonlinear vibration of sandwich plates fabricated from functionally graded materials (FGMs) resting on an elastic foundation. Higher-order shear deformation theory and Hamilton's principle are employed to obtain governing equations. The Runge-Kutta method is employed together with the commercially available mathematical software MAPLE 14 to solve the set of nonlinear dynamic governing equations. Method validity is evaluated by comparing the results of this study and those of previous research. Good agreement is achieved. The effects of temperature change on frequencies are investigated considering various temperatures and various volume fraction index values, N. As the temperature increased, the plate frequency decreased, whereas with increasing N, the plate frequency increased. The effects of the side-to-thickness ratio, c/h, on natural frequencies were investigated. With increasing c/h, the frequencies increased nonlinearly. The effects of foundation stiffness on nonlinear vibration of the sandwich plate were also studied. Backbone curves presenting the variation of maximum displacement with respect to plate frequency are presented to provide insight into the nonlinear vibration and dynamic behavior of FGM sandwich plates.

• Journal of the Institute of Convergence Signal Processing
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• v.9 no.1
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• pp.82-88
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• 2008

In this paper, Runge-Kutta (RK)-Butcher algorithm is proposed to study the periodic and oscillatory problems. Simulation results obtained using RK-Butcher algorithms and the classical fourth order Runge-Kutta (RK(4)) methods are compared with the exact solutions of a few periodic and oscillatory problems to confirm the performance of the proposed algorithm. The simulation results from RK-Butcher algorithms are always found to be very close to the exact solutions of these problems. Further, it is found that the RK-Butcher algorithm is superior when compared to RK(4) methods in terms of accuracy. The RK-Butcher algorithm can be easily implemented in a programming language and a more accurate solution may be obtained for any length of time. RK-Butcher algorithm is applicable as a good numerical algorithm for studying the problems of orbit and two body as it gives the nearly identical solutions.

• The Journal of Korean Medicine
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• v.34 no.1
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• pp.136-145
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• 2013

Objectives: Recently, Korean medicine has been explored by employing mathematical methods, which is an effort to raise Korean medicine to a higher level of scientific research. In that vein, we propose a mathematical model, analyzing the effects of seasonal cycle as an external factor in addition to the internal interactions of five-states, the engendering and the restraining. Methods: Some modified differential equations with 5-state variables were given to describe the interactions of the engendering and the restraining, and effect of seasonal cycle, and are numerically analyzed by Runge-Kutta method. We then simulated it along with time and dynamically analyzed it by Moran's I, a spatial autocorrelation. Results: We showed the effects of seasonal cycle on yin-yang five-states and applied it to the human life cycle. Conclusions: Our result is comparable to previous results in the respect that we consider the seasonal cycle and its effect on five-states, unlike others' mainly focusing on internal interaction. Furthermore, we suggest some follow-up study taking into consideration the complexity and diversity of external factors.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.1
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• pp.69-77
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• 1984

In this paper, the governing differential equations for the free vibration of uniform parabolic arches are derived on the basis of equilibrium equations of a small element of arch rib and the D'Alembert principle. A trial eigen value method is used for determining the natural frequencies and mode shapes. And the Runge-Kutta fourth order integration technique is also used in this method to perform the integration of the differential equations. A detailed study is made of the first mode for the symmetrical and anti-symmetrical vibrations of hinged arches with the Span length equal to 10 m. The effects of the rise of arch, the radius of gyration and the rotary inertia on free vibrations are presented in detail in curves and table.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2000.11a
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• pp.185-195
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• 2000

This pacer studied on the lateral motion and yaw motion of the gantry crane which is used for the automated container terminal with two driving wheel types. Though several problems are occcurred in driving of gantry crane, they are solved by the motion by the operators. But, if the gantry crane is unmanned, it is automatically controlled without any operation. There are two types, cone and flat t y pin driving wheel shape. In cone type, lateral vibration and yaw motion of crane are issued. In flat type, the collision between wheel-flange and rail or the fitting between wheel-flanges and rail is issued. Especially, the collision between wheel-flange and rail is a very critical problem in driving of unmanned gantry crane. To bring a solution to the problems, the lateral and yaw dynamic equations of the driving mechanism of gantry crane with two driving wheel types are derived. Then, we investigate the driving characteristics of gantry crane. And this study used PD(Proportional-Derivative) Controller to control the lateral displacement and yaw angle of the gantry crane. The simulation result of the driving mechanism using the Runge-Kutta Method is presented in this paper.

• Journal of Korean Society of Steel Construction
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• v.9 no.2 s.31
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• pp.221-228
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• 1997

The main purpose of this paper is to determine the dynamic optimal shapes of simple beam-columns with the constant volume. The parabolic function is chosen as the variable equation for the depth of regular polygon cross-section. The ordinary differential equation including the effect of axial load is applied to calculate the natural frequencies. The Runge-Kutta and Regula-Falsi methods are used to integrate the differential equation and compute the frequencies, respectively. Then the dynamic optimal shape whose lowest natural frequency is highest is determined by reading the critical value of the frequency versus section ratio curve plotted by the frequency data. In the numerical examples, the simple beam-columns are analysed and the numerical results of this study are shown in tables and figures.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.545-550
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• 2001

This paper studied on the lateral motion and yaw motion of the gantry crane that is used for the automated container terminal. Though several problems are occurred in driving of the gantry crane, they are solved by the motion by the operators. But, if the gantry crane is unmanned, it is automatically controlled without any operator. There are two types, cone and flat type in driving wheel shape. In cone type, the lateral vibration and yaw motion of crane are issued. In flat type, the collision between wheel-flange and rail or the fitting between wheel-flanges and rail is issued. Especially, the collision between wheel-flange and rail is a very critical problem in driving of unmanned gantry crane. To bring a solution to the problems, the lateral and yaw dynamic equations of the driving mechanism of two driving wheels are derived. Then, we investigate the driving characteristics of gantry crane. In this study, the proposed controller, based on Model Based Controller, is used to control the lateral displacement and yaw angle of the gantry crane. And the availability of the proposed controller is showed through the comparison with the result of the proposed controller and PD controller. The simulation results of the driving mechanism, using the Runge-Kutta Method that is one of the numerical analysis methods, are presented in this paper.