• Tribology and Lubricants
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• v.16 no.4
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• pp.295-301
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• 2000

The dynamic simulation of slider in hard disk drive is performed using Factored Implicit Finite Difference method. The modified Reynolds equation with Fukui and Kaneko model is employed as a governing equation. Equations of motion for the slider of three degrees of freedom are solved simultaneously with the modified Reynolds equation. The transient responses of the slider for disk step bumps and slider impulse forces are shown for various cases and are compared for the iteration algorithm and new algorithm.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.11-27
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• 2003

A fourth order in time and second order in space scheme using a finite-difference method is developed for the non-linear Boussinesq equation. For the solution of the resulting non-linear system a predictor-corrector pair is proposed. The method is analyzed for local truncation error and stability. The results of a number of numerical experiments for both the single and the double-soliton waves are given.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.449-455
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• 2007

We obtain a discrete version of a fundamental result by Yoshizawa related to the existence of almost periodic solutions of functional differential equations with finite delay.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.229-234
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• 2005

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the positive solutions of the difference equation of the form $x_{n+l} =\alpha+\frac{x_{n-1}^{p}}{x_{n}^{p}},\;\; n = 0, 1, ...$ is investigated, where all the coefficients are nonnegative real numbers.

• Korean Journal of Applied Biomechanics
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• v.27 no.1
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• pp.53-58
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• 2017

Objective: The purpose of this study was to compare the accuracy of stride time and stride length provided by a commercial APDM inertial sensor system (APDM) with the results of three dimensional motion capture system (3D motion) during treadmill walking. Method: Five healthy men participated in this experiment. All subjects walked on the treadmill for 3 minutes at their preferred walking speed. The 3D motion and the APDM were simultaneously used for extracting gait variables such as stride time and stride length. Mean difference and root mean squared (RMS) difference were used to compare the measured gait variables from the two measurement devices. The regression equation derived from the range of motion of the lower limb was also applied to correct the error of stride length. Results: The stride time extracted from the APDM was almost the same as that from the 3D motion (the mean difference and RMS difference were less than 0.0001 sec and 0.0085 sec, respectively). For stride length, mean difference and RMS difference were less than 0.1141 m and 0.1254 m, respectively. However, after correction of the stride length error using the derived regression equation, the mean difference and the RMS difference decreased to 0.0134 m and 0.0556 m or less, respectively. Conclusion: In this study, we confirmed the possibility of using the temporal variables provided from the APDM during treadmill walking. By applying the regression equation derived only from the range of motion provided by the APDM, the error of the spatial variable could be reduced. Although further studies are needed with additional subjects and various walking speeds, these results may provide the basic data necessary for using APDM in treadmill walking.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.6 s.177
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• pp.1520-1528
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• 2000

This study presents a method for determining bearing stiffness and damping coefficients of air-lubricated slider bearing, and shows influences of air-bearing surface geometry(recess depth, crown an d pivot location) on flying attitude and dynamic characteristics. To derive the dynamic lubrication equation, the perturbation method is applied to the generalized lubrication equation which based on linearized Boltzmann equation. The generalized lubrication equation and the dynamic lubrication equation are converted to a control volume formulation, and then, the static and dynamic pressure distributions are calculated by finite difference method. The recess depth and crown of the slider show significantly influence on flying attitude and dynamic characteristics comparing with those of pivot location.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.753-762
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• 2012

We study the BS-stability and the $\rho$-stability for functional difference equations with infinite delay as a discretization of Murakami and Yoshizawa's results [6] for functional differential equation with infinite delay.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.483-497
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• 2010

In this paper we study some qualitative behavior of the solutions of the difference equation $x_{n+1}=ax_n=\frac{bx_n}{cx_n-dx_{n-1}}$, n=0,1,$\ldots$, where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants with $cx_0-dx_{-1}\neq0$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.51-61
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• 2018

In this article, we mainly use Nevanlinna theory to investigate some special difference equations of malmquist type such as $f^2+({\Delta}_cf)^2={\beta}^2$, $f^2+({\Delta}_cf)^2=R$, $f{^{\prime}^2}+({\Delta}_cf)^2=R$ and $f^2+(f(z+c))^2=R$, where ${\beta}$ is a nonzero small function of f and R is a nonzero rational function respectively. These discussions extend one related result due to C. C. Yang et al. in some sense

• East Asian mathematical journal
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• v.24 no.4
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• pp.407-414
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• 2008

Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations with damping and convection terms, which describe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.