• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.125-130
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• 2007

We propose a simple and intuitive method to derive the exact convergence rate of global $L_{2}-norm$ error for strong numerical approximation of stochastic differential equations the result of which has been reported by Hofmann and $M{\"u}ller-Gronbach\;(2004)$. We conclude that any strong numerical scheme of order ${\gamma}\;>\;1/2$ has the same optimal convergence rate for this error. The method clearly reveals the structure of global $L_{2}-norm$ error and is similarly applicable for evaluating the convergence rate of global uniform approximations.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.493-502
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• 2017

We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.513-521
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• 2018

In this paper, the resonance response of spar-type floating platform in coupled heave and pitch motion is investigated using a CPU time-effective numerical method. A coupled nonlinear 2-DOF equation of motion is derived based on the potential wave theory and the rigid-body hydrodynamics. The transient responses are solved by the fourth-order Runge-Kutta (RK4) method and transformed to the frequency responses by the digital Fourier transform (DFT), and the first-order approximation of heave response is analytically derived. Through the numerical experiments, the theoretical derivation and the numerical formulation are verified from the comparison with the commercial software AQWA. And, the frequencies of resonance arising from the nonlinear coupling between heave and pitch motions are investigated and justified from the comparison with the analytically derived first-order approximation of heave response.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.165-180
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• 2001

This paper presents a new difference scheme for numerical solution of stiff system of ODE’s. The present study is mainly motivated to develop an absolutely stable numerical method with a high order of approximation. In this work a double implicit A-stable difference scheme with the sixth order of approximation is suggested. Another purpose of this study is to introduce automatic choice of the integration step size of the difference scheme which is derived from the proposed scheme and the one step scheme of the fourth order of approximation. The algorithm was tested by means of solving the Kreiss problem and a chemical kinetics problem. The behavior of the gas explosive mixture (H₂+ O₂) in a closed space with a mobile piston is considered in test problem 2. It is our conclusion that a hydrogen-operated engine will permit to decrease the emitted levels of hazardous atmospheric pollutants.

• International Journal of Automotive Technology
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• v.3 no.3
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• pp.117-122
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• 2002

Joint stiffness can affect the vibration characteristics of car body structures. Therefore, it should be included in vehicle system model. In this paper, a numerical approximation of joint stiffness is presented considering joint flexibility of thin walled beam-jointed structures. Using the proposed method, it is possible to optimize joint structures considering the change of section shapes in vehicle structures. The numerical approximation of joint stiffness is derived using the response surface method in terms of beam section properties. The study shows that joint stiffnesses can be effectively determined in designing vehicle structures.

• Transactions of the Korean Society of Automotive Engineers
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• v.9 no.3
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• pp.155-163
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• 2001

Joint stiffnesses can affect the vibrational characteristics of car body structures and, therefore, should be included in vehicle system models. In this paper, a numerical approximation of joint stiffness is presented for considering joint flexibility of thin walled beam jointed structures. Using the proposed method, it is possible to optimize joint structures considering the change of section shapes in vehicle structures. The numerical approximation of joint stiffnesses is derived using the RSM(Response Surface Method) in terms of beam section properties. The study shows that joint stiffnesses can be effectively determined in designing vehicle structure.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.2 s.245
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• pp.164-170
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• 2006

To prevent the numerical instabilities in topology optimization, continuous approximation of material distribution (CAMD) is proposed to the homogenization design method (HDM) and the simple isotropic material with penalization (SIMP) method. The continuous FE approximation of design variables including high order elements is applied to the formulation of SIMP method. Numerical examples are presented to compare the efficiency of CAMD both in HDM and SIMP.

• Korean Journal of Computational Design and Engineering
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• v.12 no.1
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• pp.27-38
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• 2007

This paper describes a multiresidual approximation method for scattered volumetric data modeling. The approximation method employs a volumetric NURBS or VNURBS as a data interpolating function and proposes two multiresidual methods as a data modeling algorithm. One is called as the residual series method that constructs a sequence of VNURBS functions and their algebraic summation produces the desired approximation. The other is the residual merging method that merges all the VNURBS functions mentioned above into one equivalent function. The first one is designed to construct wavelet-type multiresolution models and also to achieve more accurate approximation. And the second is focused on its improvement of computational performance with the save fitting accuracy for more practical applications. The performance results of numerical examples demonstrate the usefulness of VNURBS approximation and the effectiveness of multiresidual methods. In addition, several graphical examples suggest that the VNURBS approximation is applicable to various applications such as surface modeling and fitting problems.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.4
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• pp.475-480
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• 2004

Function approximation is one of the most important and active research fields in design optimization. Accurate function approximations can reduce the repetitive computational effort fur system analysis. So this study presents an enhanced two-point diagonal quadratic approximation method. The proposed method is based on the Two-point Diagonal Quadratic Approximation method. But unlike TDQA, the suggested method has two quadratic terms, the diagonal term and the correction term. Therefore this method overcomes the disadvantage of TDQA when the derivatives of two design points are same signed values. And in the proposed method, both the approximate function and derivative values at two design points are equal to the exact counterparts whether the signs of derivatives at two design points are the same or not. Several numerical examples are presented to show the merits of the proposed method compared to the other forms used in the literature.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.861-873
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• 2005

In this paper we approximate a cylindrical helix by bi-conic and bi-quadratic Bezier curves. Each approximation method is $G^1$ end-points interpolation of the helix. We present a sharp upper bound of the Hausdorff distance between the helix and each approximation curve. We also show that the error bound has the approximation order three and monotone increases as the length of the helix increases. As an illustration we give some numerical examples.