• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.447-456
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• 1997

In this paper an accurate algorithm for the method of successive approximations for near-parabolic orbits is established symbolically. Numerical applications are given for motion predictions at fifteen epochs between the years 66 to 1835 for Halley's comet. and at fifteen epochs between the years 1417 to 1782 for Encke's comet. Comparisons with the standard Gauss method [4] show that the present algorithm is very accurate and efficient for motion pred-ications of near-parabolic orbits.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.699-721
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• 2015

This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.585-598
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• 2014

In this paper we consider the nonlinear parabolic problems with mixed boundary condition. Under comparatively mild conditions of the coefficients related to the problem, we construct the discontinuous Galerkin approximation of the solution to the nonlinear parabolic problem. We discretize spatial variables and construct the finite element spaces consisting of discontinuous piecewise polynomials of which the semidiscrete approximations are composed. We present the proof of the convergence of the semidiscrete approximations in $L^{\infty}(H^1)$ and $L^{\infty}(L^2)$ normed spaces.

• Journal of the Korean Society for Precision Engineering
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• v.31 no.4
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• pp.319-326
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• 2014

Accurate estimation of the robot's position has an important role in autonomous navigation. Odometry is one of the most widely used techniques for mobile robot positioning. However, odometry has a well-known drawback that the position errors are accumulated when the travel distance increases. The UMBmark method is the conventional odometry calibration scheme for two wheel differential mobile robots. In the UMBmark method, the approximations for small angles are used in order to simplify the calculations. In this paper, we propose the new calibration scheme by using experimental orientation errors. Kinematic parameters can be calculated accurately without approximations by using experimental orientation errors. The numerical simulation and experimental results show that the odometry accuracy can be improved by the proposed method.

• Korea-Australia Rheology Journal
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• v.12 no.2
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• pp.125-133
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• 2000

The present work is aimed at performing injection molding filling simulation of fiber suspension in polymer based matrix. The numerical simulation incorporates the coupling effect between the flow field and the fiber orientation state together with in-plane velocity gradient effect with recently proposed closure approximations. Predicted orientation components are compared with available experimental data of a film-gated strip and a center-gated disk. Predictions with IBOF closure approximation show excellent behaviors with regard to accuracy and numerical efficiency. However, predicted results seem to have consistent errors in comparison with experimental data. Diffusivity term which accounts for fiber-fiber interaction might have to be modified.

• Journal of Korean Institute of Industrial Engineers
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• v.34 no.1
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• pp.1-12
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• 2008

The Kanban system in Just-In-Time (JIT) production is very effective in reducing the inventories when consumption rate of the final product is relatively stable. When large fluctuations exist in the consumption rate, a new production ordering policy in which the production order quantity is determined by smoothing the demands exponentially is more suitable. This new ordering policy has not been investigated sufficiently. In this research, a multi-stage production and inventory system with stock points for materials and finished items located at each stage is considered. Approximations of average inventories at each stage in the system are derived theoretically. Numerical simulations are carried out to assess the accuracy of approximations and to evaluate the effectiveness of the new ordering policy as compared with the Kanban system. As a result, it is shown that the new ordering policy can achieve significantly lower inventory costs than the original Kanban system. The new ordering policy thus emerges as a key concept for an effective supply chain management.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.1191-1195
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• 2007

Many approximate models for interaction between a flexible structure and an infinite external acoustic medium have been developed for a long time. Among them, Doubly Asymptotic Approximations (DAAs) are very well known approximations. But, it has shortcomings in intermediate frequency range and can't fully describe the acoustic medium. So, this paper presents the modified approximation by applying the retarded and advanced potentials to Kirchhoff's formula. It describes the external acoustic medium more in detail and shows a good result in early time transient responses when it was applied to a spherical shell. Through a spherical shell interacting with external acoustic medium, the transient responses for the proposed model is compared to Huang's exact solution and DAA2.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1127-1144
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• 2013

In this paper, we consider the error estimates of the numerical solutions of a class of fourth order linear-quadratic elliptic optimal control problems by using mixed finite element methods. The state and co-state are approximated by the order $k$ Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order $k(k{\geq}1)$. $L^2$ and $L^{\infty}$-error estimates are derived for both the control and the state approximations. These results are seemed to be new in the literature of the mixed finite element methods for fourth order elliptic control problems.

• The Korean Journal of Applied Statistics
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• v.22 no.6
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• pp.1345-1353
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• 2009

We introduce a simple methodology, so-called generalized gamma-polynomial approximation, based on moment-matching technique to approximate survival and hazard functions in the context of parametric survival analysis. We use the generalized gamma-polynomial approximation to approximate the density and distribution functions of convolutions and finite mixtures of random variables, from which the approximated survival and hazard functions are obtained. This technique provides very accurate approximation to the target functions, in addition to their being computationally efficient and easy to implement. In addition, the generalized gamma-polynomial approximations are very stable in middle range of the target distributions, whereas saddlepoint approximations are often unstable in a neighborhood of the mean.

• Structural Engineering and Mechanics
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• v.18 no.5
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• pp.565-589
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• 2004

The present paper concerns the macroscopic overall description of rheologic properties for steel wire and synthetic fibre cables under variable loading actions according to non-linear creep and/or relaxation theory. The general constitutive equations of non-linear creep and/or relaxation of tension elements - cables under one-step and the variable stress or strain inputs using the product and two types of additive approximations of the kernel functions are presented in the paper. The derived non-linear constitutive equations describe a non-linear rheologic behaviour of the cables for a variable stress or strain history using the kernel functions determined only by one-step - constant creep or relaxation tests. The developed constitutive equations enable to simulate and to predict in a general way non-linear rheologic behaviour of the cables under an arbitrary loading or straining history. The derived constitutive equations can be used for the various tension structural elements with the non-linear rheologic properties under uniaxial variable stressing or straining.