• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.301-311
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• 2015

In this paper, we present the error control techniques for the error correction methods (ECM) which is recently developed by P. Kim et al. [8, 9]. We formulate the local truncation error at each time and calculate the approximated solution using the solution and the formulated truncation error at previous time for achieving uniform error bound which enables a long time simulation. Numerical results show that the error controlled ECM provides a clue to have uniform error bound for well conditioned problems [1].

• Proceedings of the Korean Nuclear Society Conference
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• 1997.10a
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• pp.79-84
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• 1997

동특성 분석 코드 시스템 PANBOX2는 시간에 대한 미분을 Implicit Euler 방법을 사용하여 근사한다. 이 경우 Local Truncation Error는 중성자속의 이차 미분에 비례한다. Time-Step-Doubling 기법을 이용하여 Local Truncation Error의 근사치를 구하고 이를 이용하여 Time Step Size를 조절해 주는 방법을 동특성 분석 코드 시스템 PANBOX2에 도입하였다. LRA와 NEACRP 제어봉 인출사고 검증문제에 대한 분석 결과, PANBOX2 시스템의 기존 방법에 비해 효과적으로 Time Step을 제어하였으며 보다 정확한 결과를 얻을 수 있었다.

• ETRI Journal
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• v.31 no.1
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• pp.42-50
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• 2009

A new method for simulating voltage and current distributions in transmission lines is described. It gives the time domain solution of the terminal voltage and current as well as their line distributions. This is achieved by treating voltage and current distributions as distributed state variables (DSVs) and turning the transmission line equation into an ordinary differential equation. Thus the transmission line is treated like other lumped dynamic components, such as capacitors. Using backward differentiation formulae for time discretization, the DSV transmission line component is converted to a simple time domain companion model, from which its local truncation error can be derived. As the voltage and current distributions get more complicated with time, a new piecewise exponential with controllable accuracy is invented. A segmentation algorithm is also devised so that the line is dynamically bisected to guarantee that the total piecewise exponential error is a small fraction of the local truncation error. Using this approach, the user can see the line voltage and current at any point and time freely without explicitly segmenting the line before starting the simulation.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.45-57
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• 2001

A parametric scheme is proposed for the numerical solution of the nonlinear Boussinesq equation. The numerical method is developed by approximating the time and the space partical derivatives by finite-difference re placements and the nonlinear term by an appropriate linearized scheme. The resulting finite-difference method is analyzed for local truncation error and stability. The results of a number of numerical experiments are given for both the single and the double-soliton wave. AMS Mathematics Subject Classification : 65J15, 47H17, 49D15.

• 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.

• Honam Mathematical Journal
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• v.32 no.3
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• pp.481-491
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• 2010

In this paper, we investigate a generalization of the Adams-Bashforth method by using the Taylor's series. In case of m-step method, the local truncation error can be expressed in terms of m - 1 coefficients. With an appropriate choice of coefficients, the proposed method has produced much smaller error than the original Adams-Bashforth method. As an application of the generalized Adams-Bashforth method, the accuracy performance is demonstrated in the satellite orbit prediction problem. This implies that the generalized Adams-Bashforth method is applied to the orbit prediction of a low-altitude satellite. This numerical example shows that the prediction of the satellite trajectories is improved one order of magnitude.

• Earthquakes and Structures
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• v.14 no.1
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• pp.45-53
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• 2018

A family of the structure-dependent methods seems very promising for time integration since it can simultaneously have desired numerical properties, such as unconditional stability, second-order accuracy, explicit formulation and numerical dissipation. However, an unusual overshoot, which is essentially different from that found by Goudreau and Taylor in the transient response, has been experienced in the steady-state response of a high frequency mode. The root cause of this unusual overshoot is analytically explored and then a remedy is successfully developed to eliminate it. As a result, an improved formulation of this family method can be achieved.

• Structural Engineering and Mechanics
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• v.60 no.1
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• pp.149-162
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• 2016

Structure-dependent integration methods seem promising for structural dynamics applications since they can integrate unconditional stability and explicit formulation together, which can enable the integration methods to save many computational efforts when compared to an implicit method. A newly developed structure-dependent integration method can inherit such numerical properties. However, an unusual overshooting behavior might be experienced as it is used to compute a forced vibration response. The root cause of this inaccuracy is thoroughly explored herein. In addition, a scheme is proposed to modify this family method to overcome this unusual overshooting behavior. In fact, two improved formulations are proposed by adjusting the difference equations. As a result, it is verified that the two improved formulations of the integration methods can effectively overcome the difficulty arising from the inaccurate integration of the steady-state response of a high frequency mode.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.699-713
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• 2022

This paper proposes a hybrid successive over-relaxation iterative method for the numerical solution of a nonlinear diffusion in a one-dimensional porous medium. The considered mathematical model is discretized using a computational complexity reduction scheme called half-sweep finite differences. The local truncation error and the analysis of the stability of the scheme are discussed. The proposed iterative method, which uses explicit group technique and modified successive over-relaxation, is formulated systematically. This method improves the efficiency of obtaining the solution in terms of total iterations and program elapsed time. The accuracy of the proposed method, which is measured using the magnitude of absolute errors, is promising. Numerical convergence tests of the proposed method are also provided. Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.2
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• pp.338-348
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• 1988

This study presents an analysis of periodic heat diffusion in an annular fin with uniform thickness. When the temperature of the fin base is changed in the form of a sinusoidal function, the exact temperature solution can be obtained by Laplace transformation in terms of the dimensionless parameters in the infinite series. Local heat flux and average heat flux, local fin efficiency and average fin efficiency were obtained. Particularly, the table of eigenvalues that are the indispensable condition in solving the heat transfer problem of annular fin in a transient state with convection phenomena at the fin edge is provided. The tables of heat fluxes and average heat fluxes, fin efficiencies and average fin efficiencies are also provided from the computed results. Also, substituting the variations of dimensionless parameters into the these exact solutions, the characteristics of these response are investigated.