• Journal of information and communication convergence engineering
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• v.12 no.1
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• pp.39-45
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• 2014

A numerical method for solving Hamiltonian equations is said to be symplectic if it preserves the symplectic structure associated with the equations. Various symplectic methods are widely used in many fields of science and technology. A symplectic method preserves an approximate Hamiltonian perturbed from the original Hamiltonian. It theoretically supports the effectiveness of symplectic methods for long-term integration. Although it is also related to long-term integration, numerical stability of symplectic methods have received little attention. In this paper, we consider explicit symplectic methods defined for Hamiltonian equations with Hamiltonians of the special form, and study their numerical stability using the harmonic oscillator as a test equation. We propose a new stability criterion and clarify the stability of some existing methods that are visually based on the criterion. We also derive a new method that is better than the existing methods with respect to a Courant-Friedrichs-Lewy condition for hyperbolic equations; this new method is tested through a numerical experiment with a nonlinear wave equation.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.11
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• pp.1075-1082
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• 2004

This research demonstrates the shock response analysis of a head disk assembly subjected to a half-sine shock pulse in the axial direction. In case of disk analysis, the numerical method presented by Barasch and Chen is used. Galerkin method is used with mode shape by numerical method. Head-suspension system is modeled as the cantilever in order to get simulation results. Simulation results of HDA are calculated by Runge-Kutta method. Finally, shock responses of head and disk are analyzed according to the change of the rotating speed of the disk.

• Structural Engineering and Mechanics
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• v.30 no.5
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• pp.593-602
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• 2008

This paper presents a new linearization algorithm to find the periodic solutions of the Duffing equation, under harmonic loads. Since the Duffing equation models a single degree of freedom system with a cubic nonlinear term in the restoring force, finding its periodic solutions using classical harmonic balance (HB) approach requires numerical integration. The algorithm developed in this paper replaces the integrals appearing in the classical HB method with triangular matrices that are evaluated algebraically. The computational cost of using increased number of frequency components in the matrixbased linearization approach is much smaller than its integration-based counterpart. The algorithm is computationally efficient; it only takes a few iterations within the region of convergence. An example comparing the results of the linearization algorithm with the "exact" solutions from a 4th order Runge- Kutta method are presented. The accuracy and speed of the algorithm is compared to the classical HB method, and the limitations of the algorithm are discussed.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.175-184
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• 1999

Along with the computation and analysis for nonlinear system being more and more involved in the fields such as automation control electronic technique and electrical power system the nonlin-ear theory has become quite a attractive field for academic research. In this paper we derives the solutions for state equation of nonlinear system by using the inverse operator expression of the so-lutions is obtained. An actual computation example is given giving a comparison between IOM and Runge-kutta method. It has been proved by our investigation that IOM has some distinct advantages over usual approximation methods in that it is computationally con-venient rapidly convergent provides accurate solutions not requiring perturbation linearization or the massive computation inherent in discrietization methods such as finite differences. So the IOM pro-vides an effective method for the solution of nonlinear system is of potential application valuable in nonlinear computation.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.167-177
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• 2012

In this article, we propose exponentially fitted error correction methods(EECM) which originate from the error correction methods recently developed by the authors (see [10, 11] for examples) for solving nonlinear stiff initial value problems. We reduce the computational cost of the error correction method by making a local approximation of exponential type. This exponential local approximation yields an EECM that is exponentially fitted, A-stable and L-stable, independent of the approximation scheme for the error correction. In particular, the classical explicit Runge-Kutta method for the error correction not only saves the computational cost that the error correction method requires but also gives the same convergence order as the error correction method does. Numerical evidence is provided to support the theoretical results.

• Journal of the Korean Society for Railway
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• v.9 no.1 s.32
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• pp.63-68
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• 2006

This paper proposes a fast Fourier transform(FFT)-based spectral analysis method(SAM) for the dynamic responses of the linear discrete dynamic models with non-proportional damping. The SAM was developed by using discrete Fourier transform(DFT)-theory. To verify the proposed SAM, a three-DOF system with non-proportional viscous damping is considered as an illustrative example. The present SAM is evaluated by comparing the dynamic responses obtained by SAM with those obtained by Runge-Kutta method.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.51 no.10
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• pp.560-567
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• 2002

This paper presents the calculation of opening characteristics for puffer GCB with the equations of the flow field and the motion of the driving mechanism. To obtain the stroke curve, the motion equation is solved simultaneously with the Euler equations. For a given Piston location, the flow field is solved. The pressure inside the Puffer chamber is then used to calculate the moving velocity and the new position of the piston. The FVFLIC method is employed to solve the axisymmetric Euler equations and the motion equation is solved by the Runge-Kutta method. The method is applied to the puffer GCB model and the stroke curve and the pressure rise in puffer chamber under no load condition are compared with the measured ones.

• Structural Engineering and Mechanics
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• v.56 no.5
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• pp.797-811
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• 2015

An analytical-computational method along with finite element analysis (FEA) has been employed to analyse the dynamic behaviour of deteriorated structures excited by time- varying mass. The present analysis is focused on the comparative study of a double cracked beam with inclined edge cracks and transverse open cracks subjected to traversing mass. The assumed computational method applied is the fourth order Runge-Kutta method. The analysis of the structure has been carried out at constant transit mass and speed. The response of the structure is determined at different crack depth and crack inclination angles. The influence of the parameters like crack depth and crack inclination angles are investigated on the dynamic behaviour of the structure. The results obtained from the assumed computational method are compared with those of the FEA for validation and found good agreements with FEA.

• Journal of Ship and Ocean Technology
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• v.5 no.1
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• pp.38-54
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• 2001

A finite difference method for calculating turbulent flow and surface wave fields around a ship model is evaluated through the comparison with the experimental data of a Series 60 $C_B$=0.6 ship model. The method solves the Reynolds-averaged Navior-Stokes Equations using the non-staggered grid system, the four-stage Runge-Kutta scheme for the temporal integration of governing equations and the Bladwin-Lomax model for the turbulence closure. The free surface waves are captured by solving the equation of the kinematic free-surface condition using the Lax-Wendroff scheme and free-surface conforming grids are generated at each time step so that one of the grid surfaces coincides always with the free surface. The computational results show an overall close agreement with the experimental data and verify that the present method can simulate well the turbulent boundary layers and wakes as well as the free-surface waves.

• Proceedings of the SAREK Conference
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• 2006.06a
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• pp.116-121
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• 2006

Numerical simulations for dendritic growth of crystals are conducted in this study by the level set method. The effect of order of difference is tested for reinitialization error in simple problems and authors founded in case of 1st order of difference that very fine grids have to be used to minimize the error and higher order of difference is desirable to minimize the reinitialization error The 2nd and 4th order Runge-Kutta scheme in time and 3rd and 5th order of WENO schemes with Godunov scheme are applied for space discretization. Numerical results are compared with the analytical theory, phase-field method and other researcher's level set method.