• Earthquakes and Structures
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• v.7 no.1
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• pp.1-15
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• 2014

In this paper we consider three different cases and we apply Variational Approach (VA) to solve the non-natural vibrations and oscillations. The method variational approach does not demand small perturbation and with only one iteration can lead to high accurate solution of the problem. Some patterns are presented for these three different cease to show the accuracy and effectiveness of the method. The results are compared with numerical solution using Runge-kutta's algorithm and another approximate method using energy balance method. It has been established that the variational approach can be an effective mathematical tool for solving conservative nonlinear dynamical equations.

• Journal of the Korea Society of Computer and Information
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• v.8 no.3
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• pp.66-72
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• 2003

An ordinary differential equation in analytical numerics is utilized to some applications, for example, physics, mechanical engineering, electrical engineering, thermodynamics and etc. But this equation has problems a lots to process in the real time processing by software method. This paper is proposed a systolic Arrays architecture for solving the Runge-Kutta method. it is one of method for solving an ordinary differential equation. the proposed its architecture is very high speed and regular. this hardware proposed in this paper may be part of the mathematical problem solver's tool kit in the future and may be available to many applications in the engineering.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.1-28
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• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.

• Structural Engineering and Mechanics
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• v.75 no.2
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• pp.239-246
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• 2020

In this paper, a novel analytical method, Max-Min Approach (MMA), has been presented and applied to consider the nonlinear vibration of dry cask storage systems. The nonlinear governing equation of the structure has been developed using the shell theory. The MMA results are compared with numerical solutions derived by Runge-Kutta's Method (RKM). The results indicate a satisfying agreement between MMA and numerical solutions. Parametric studies have been conducted on the nonlinear frequency of dry casks. The phase-plan of the problem is also presented and discussed. The proposed approach can potentially ca be extended to highly nonlinear problems.

• Magazine of the Korean Society of Agricultural Engineers
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• v.36 no.2
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• pp.56-66
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• 1994

Numerical methods are developed to obtain the buckling loads and to analyze the postbuckling behavior of the tapered steel piles. The nondimensional differential equations governing the elastica of the buckled piles are derived by the third order theory and solved numerically. The Runge-Kutta method is used to solve the differential equations, and the bisection method is used to obtain the buckling loads and the reaction moments of the clamped ends. Both the linear and stepped taper of the steel piles are considered as the variable crosssection in the differential equations. As the numerical results, the equilibrium paths, the buckling loads vs. section ratio curves and the typical elastica and the bending moment diagrams of the buckled piles are presented in figures. Experimental studies that complement the theoretical results are presented. It is expected that the numerical methods developed in this study for calculating the buckling loads and analyzing the postbuckling behavior of the steel piles are used in the structural and foundation engineering.

• Journal of Ocean Engineering and Technology
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• v.14 no.1
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• pp.67-73
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• 2000

The dynamic behavior of a moving elastic body system with three constant velocitics on a simple beam with an axial load is analyzed by numerical method. A moving elastic body system is composed of an elastic body and a suspension unit with two unsprung masses. The governing equations are derived with an aid of Lagrange's equation. These equation are solved by Runge-Kutta method. The damping coefficients a spring constants of the suspension unit the force circular frequency on a moving elastic body the velocity of a moving elastic body system. These effects are more important in the high modes of a simple beam.

• The KIPS Transactions:PartB
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• v.13B no.1 s.104
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• pp.15-20
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• 2006

This paper describes research on intelligent game character through performance enhancements of physics engine in computer games. The algorithm that recognizes the physics situation uses momentum back-propagation neural networks. Also, we present an experiment and its results, integration methods that display optimum performance based on the physics situation. In this experiment on integration methods, the Euler method was shown to produce the best results in terms of fps in a simulation environment with collision detection. Simulation with collision detection was shown similar fps for all three methods and the Runge-kutta method was shown the greatest accuracy. In the experiment on physics situation recognition, a physics situation recognition algorithm where the number of input layers (number of physical parameters) and output layers (destruction value for the master car) is fixed has shown the best performance when the number of hidden layers is 3 and the learning count number is 30,000. Since we tested with rigid bodies only, we are currently studying efficient physics situation recognition for soft body objects.

• Journal of computational fluids engineering
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• v.19 no.3
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• pp.91-97
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• 2014

A high resolution numerical method aimed at solving cavitating flow was proposed and applied to gas-liquid two-phase shock tube problem with arbitrary void fraction. The present method with compressibility effects employs a finite-difference 4th-order Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL TVD scheme. The Jacobian matrix from the inviscid flux of constitute equation is diagonalized analytically and the speed of sound for the two-phase media is derived by eigenvalues. So that the present method is appropriate for the extension of high order upwind schemes based on the characteristic theory. By this method, a Riemann problem for Euler equations of one dimensional shock tube was computed. Numerical results of high speed flow phenomena such as detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media and some data related to computational efficiency are made. Comparisons of predicted results and solutions at isothermal condition are provided and discussed.

• Journal of Ocean Engineering and Technology
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• v.9 no.2
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• pp.53-60
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• 1995

A multi-leg spread mooring system for floating offshore structures is important, but the multi-leg static analysis is complicated due to the nonlinear behavior of each line and the effect of current which affects each line differently. The pretensioned position of the multi-leg mooring system obtained from the static equilibrium condition changes into a different position due to external loads and current. In this paper, the new position and the static tension at each line are caculated. The relation between the initial static equilibrium position and the new position due to the external loads is expressed in terms of the Taylor's series expansion. The Runge-Kutta $4^{th}$ method is employed in analyzing the 3-dimensional static cable nonlinear equations.

• Proceedings of the KIEE Conference
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• 1991.07a
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• pp.682-686
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• 1991

The purpose of a solar tracking system (STS) is to control the attitude of a space vehicle so that it will track the sun with high accuracy. In this paper, the literature of tracking of the sun in a plane is surveyed and a control modeling for the analysis of STS is presented by simultaneous transfer functions and state-space equations. Also a program for obtaining state variables by the single term Walsh series(STWS) approach is developed. The proposed approach is much simpler in analysis and easier in implementation than the Runge-Kutta numerical integration Method. The results of computer simulation are shown for the dynamic behaviors of vehicle axis, armature-controlled dc motor and controller of STS via a Runge-Kutta method and a single term Walsh series approach, respectively.