• Journal of Mechanical Science and Technology
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• 제17권5호
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• pp.637-646
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• 2003

In the previous study, the inverse perturbation method was used to identify structural damages. Because all unmeasured DOFs were considered as unknown variables, considerable computational effort was required to obtain reliable results. Thus, in the present study, a system condensation method is used to transform the unmeasured DOFs into the measured DOFs, which eliminates the remaining unmeasured DOFs to improve computational efficiency. However, there may still arise a numerically ill-conditioned problem, if the system condensation is not adequate for numerical Programming or if the system condensation is not recalibrated with respect to the structural changes. This numerical problem is resolved in the present study by adopting more accurate accelerated improved reduced system (AIRS) as well as by updating the transformation matrix at every step. The criterion on the required accuracy of the condensation method is also proposed. Finally, numerical verification results of the present accelerated inverse perturbation method (AIPM) are presented.

• Bulletin of the Korean Chemical Society
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• 제10권6호
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• pp.529-535
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• 1989

A general perturbation series solution of the Smoluchowski equation is applied to investigate the rate of recombination and the remaining probability of a pair of particles in liquids. The radiative boundary condition is employed and the convergence of the perturbation series is analyzed in terms of a convergene factor in time domain. The upper bound to the error introduced by the n-th order perturbation scheme is also evaluated. The long time behaviors of the rate of recombination and the remaining probability are found to be expressed in closed forms if the perturbation series is convergent. A new and efficient method of purely numerical integration of the Smoluchowski equation is proposed and its results are compared with those obtained by the perturbation method. For the two cases where the interaction between the particles is given by (i) the Coulomb potential and (ii) the shielded Coulomb potential, the agreement between the two results is found to be excellent.

• 한국소음진동공학회논문집
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• 제23권8호
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• pp.734-741
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• 2013

In contrast of external excitations, parametric excitations can produce a large response when the excitation frequency is away from the linear natural frequencies. The Mathieu equation is the simplest differential equation with periodic coefficients, which lead to the parametric excitation. The Mathieu equation may have the unbounded solutions. This work conducted the stability analysis for the Mathieu equation, using Floquet theory and numerical method. Using Lindstedt's perturbation method, harmonic solutions of the Mathieu equation and transition curves separating stable from unstable motions were obtained. Using Floquet theory with numerical method, stable and unstable regions were calculated. The numerical method had the same transition curves as the perturbation method. Increased stable regions due to the inclusion of damping were calculated.

• Korean Journal of Mathematics
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• 제22권1호
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• pp.123-131
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• 2014

The purpose of this paper is to study the perturbation analysis of the matrix equation $X=I-A^*X^{-1}A+B^*X^{-1}B$. Based on the matrix differentiation, we give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the shrpness of the perturbation bound.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1279-1292
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• 2009

In this paper, a numerical method that uses standard finite difference scheme defined on Shishkin mesh for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a discontinuous source term is presented. An error estimate is derived to show that the method is uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented to illustrate the theoretical results.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 2003년도 학술대회지
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• pp.210-214
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• 2003

The static and dynamic characteristics of HDD slider with ulta-low flying height are analyzed using Direct Numerical method with Boundary Fitted Coordinate System. The slip flow effect is considered using the Boltzmann equation solution in a form of the flow rate database. The air film stiffness and damping are evaluated by the small perturbation method.

• Steel and Composite Structures
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• 제17권1호
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• pp.123-131
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• 2014

In this paper we have considered the vibration of parametrically excited oscillator with strong cubic positive nonlinearity of complex variable in nonlinear dynamic systems with forcing based on Mathieu-Duffing equation. A new analytical approach called homotopy perturbation has been utilized to obtain the analytical solution for the problem. Runge-Kutta's algorithm is also presented as our numerical solution. Some comparisons between the results obtained by the homotopy perturbation method and Runge-Kutta algorithm are shown to show the accuracy of the proposed method. In has been indicated that the homotopy perturbation shows an excellent approximations comparing the numerical one.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• 제어로봇시스템학회논문지
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• 제12권3호
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• pp.201-207
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• 2006

A robust Kalman filtering method for uncertain stochastic systems is suggested by adopting a perturbation estimation process which is to reconstruct total uncertainty with respect to the nominal state transition equation. The predictor and corrector of discrete Kalman filter are reformulated with the perturbation estimator. Successively, the state and perturbation estimation error dynamics and the corresponding error covariance propagation equations are derived as well. Finally we have the recursive algorithm of Combined Kalman Filter-Perturbation Estimator (CKF). The proposed combined Kalman filter-perturbation estimator has the property of integrating innovations and the adaptation capability to system uncertainties. A numerical example is shown to demonstrate the effectiveness of the proposed scheme.

• Communications for Statistical Applications and Methods
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• 제23권1호
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• pp.21-32
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• 2016

We study asymptotic expansion formulae for numerical computation of Greeks (i.e. sensitivity) in finance. Our approach is based on the integration-by-parts formula of the Malliavin calculus. We propose asymptotic expansion of Greeks for a stochastic volatility model using the Greeks formula of the Black-Scholes model. A singular perturbation method is applied to derive asymptotic Greeks formulae. We also provide numerical simulation of our method and compare it to the Monte Carlo finite difference approach.