• Journal of Positioning, Navigation, and Timing
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• 제8권4호
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• pp.201-208
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• 2019

Numerical integration is necessary for satellite orbit determination and its prediction. The numerical integration algorithm can be divided into single-step and multi-step method. There are lots of single-step and multi-step methods. However, the Runge-Kutta method in single-step and the Adams method in multi-step are generally used in global navigation satellite system (GNSS) satellite orbit. In this study, 4th and 8th order Runge-Kutta methods and various order of Adams-Bashforth-Moulton methods were used for GLObal NAvigation Satellite System (GLONASS) orbit integration using its broadcast ephemeris and these methods were compared with international GNSS service (IGS) final products for 7days. As a result, the RMSE of Runge-Kutta methods were 3.13m and 4th and 8th order Runge-Kutta results were very close and also 3rd to 9th order Adams-Bashforth-Moulton results. About result of computation time, this study showed that 4th order Runge-Kutta was the fastest. However, in case of 8th order Runge-Kutta, it was faster than 14th order Adams-Bashforth-Moulton but slower than 13th order Adams-Bashforth-Moulton in this study.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권4호
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• pp.238-266
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• 2013

The Interaction Picture (IP) method is a valuable alternative to Split-step methods for solving certain types of partial differential equations such as the nonlinear Schr$\ddot{o}$dinger equation or the Gross-Pitaevskii equation. Although very similar to the Symmetric Split-step (SS) method in its inner computational structure, the IP method results from a change of unknown and therefore do not involve approximation such as the one resulting from the use of a splitting formula. In its standard form the IP method such as the SS method is used in conjunction with the classical 4th order Runge-Kutta (RK) scheme. However it appears to be relevant to look for RK scheme of higher order so as to improve the accuracy of the IP method. In this paper we investigate 5th order Embedded Runge-Kutta schemes suited to be used in conjunction with the IP method and designed to deliver a local error estimation for adaptive step size control.

• 한국해양공학회지
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• 제4권2호
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• pp.73-84
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• 1990

A circular cylinder is oscillated in th otherwise quiescent viscous fluid. Numerical analysis performed for this problem by using the fourth-order Runge-kutta method for the unsteady Navier-stokes equations. For K(Kelegan-Carpenter's No.)=5, the flow developed symmetrically, while for K=10, it revealed random patterns. The coefficient of the rms force is overestimated by 20-30% compared with the experimental result.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.383-388
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• 1991

This paper analizes two numerical integration methods, both based on the Runge Kutta 4-th order formula for deterministic systems, for digital simulation of a differential equation driven by white noise. It is shown that a "standard' Runge Kutta method for stochasitic systems yields solutions of Stratonovich differential equations, while Riggs and Phillips' method results in solutions of Ito differential equations. Therefore the white noise differential equation must be converted into the equivalent Ito equation before the latter method is used. Digital simulation results for a simple differential equation are also presented.nted.

• 한국전산유체공학회지
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• 제15권2호
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• pp.55-61
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• 2010

A dependence of weighting parameter in preconditioning method for solving low Mach number flow with incompressible flow nature is investigated. The present preconditioning method employs a finite-difference method applied Roe‘s flux difference splitting approximation with the MUSCL-TVD scheme and 4th-order Runge-Kutta method in curvilinear coordinates. From the computational results of benchmark flows through a 2-D backward-facing step duct it is confirmed that there exists a suitable value of the weighting parameter for accurate and stable computation. A useful method to determine the weighting parameter is introduced. With this method, high accuracy and stable computational results were obtained for the flow with low Mach number in the range of Mach number less than 0.3.

• 한국해양공학회지
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• 제4권2호
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• pp.223-223
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• 1990

A circular cylinder is oscillated in th otherwise quiescent viscous fluid. Numerical analysis performed for this problem by using the fourth-order Runge-kutta method for the unsteady Navier-stokes equations. For K(Kelegan-Carpenter''s No.)=5, the flow developed symmetrically, while for K=10, it revealed random patterns. The coefficient of the rms force is overestimated by 20-30% compared with the experimental result.

• 한국측량학회지
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• 제28권6호
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• pp.573-578
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• 2010

위성항법시스템에서 정확한 위성궤도결정 기술은 측위 정확도 향상의 필수적인 조건이다. 이 연구에서는 GLONASS의 방송궤도력과 4차 Runge-Kutta 수치적분법을 이용하여 위성좌표를 결정하였으며, 적분간격과 적분시간에 따른 위성궤도의 정확도를 비교하였다. 적분간격에 따른 위성궤도 정확도분석결과, 적분간격이 l초일 때와 300초일 때의 3차원 RMS 오자의 차이가 3cm에 불과한 반면 처리시간은 100배 이상 향상되었다. 적분시간에 따른 위성좌표의 3차원 RMS 오차는 적분시간이 30분, 150분, 300분일 때 각각 8.3m, 187.3m, 661.5m로 나타났으며, 이를 통해 적분시간을 짧게 할수록 정확도가 향상되는 것을 확인하였다. 따라서 이 연구에서는 GLONASS 측위를 위한 위성좌표 결정의 정확도 향상을 위해 적분시간을 최소화할 수 있는 Forward와 Backward 적분을 적용하는 방안을 제안하였으며, 이와 같은 방법을 사용할 경우 5m이하의 위성좌표 산출 정확도를 확보할 수 있다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2005년도 춘계 학술대회논문집
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• pp.197-201
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• 2005

According to operating conditions of each engine, a PCV valve has various flow rates and pressure characteristic. In a developed country, it has been developing by a computational design simulation. But, Korean companies have no ability of technical design for a PCV valve. So, they depend on their experiments and copy the designs of foreign companies when they need to design new PCV valves. These problems cause increase of error rate and take much time. Hence, optimal design for a PCV valve is needed to secure for continuous competition against foreign automobile companies. In this study, we used 4th order Runge-Kutta method for the prediction of spool movements and applied Bernoulli's equation for the determination of flow area. A spool geometry and spool displacement were predicted to be satisfied in comparison with their experiment.

• 자동차안전학회지
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• 제5권1호
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• pp.25-30
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• 2013

The main purpose of this research is to predict dynamic behavior of door locking system for side impact safety and the design process to avoid door opening is introduced. The equations of motion that represent the system are obtained from the energy equation. From them, the motion of door handle is predicted by using Runge-Kutta $4^{th}$ order method and the simulation result is compared with the real crash data. Also, the design guide to define the properties of door locking system from the standpoint of avoiding door opening phenomenon is introduced.

• 공업화학
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• 제9권7호
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• pp.1079-1084
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• 1998

우레탄 생성반응의 동역학을 조사하기 위해 지방족 이소시아네이트인 4,4'-dihexyl methane diisocyanate($H_{12}MDI$)와 1 관능기 알코올인 n-hexanol간의 반응을 실험적 측정과 수학적 모델링을 통해 연구하였다. 실험은 dibutyltin dilaurate(DBTDL)을 촉매로, 톨루엔을 용매로 온도, 촉매농도, [NCO]/[OH] 비 등을 변화시키면서 실시하였고, 반응동역학은 NCO기와 OH기의 반응에 의한 우레탄 생성반응 및 NCO기와 우레탄간의 반응에 의한 allophanate 생성반응 등 2가지 2차반응식으로 모사하였다. 반응속도상수는 Runge-Kutta 4th order 방법에 의한 전산모사방법으로 계산하였다. 대부분의 조건에서 실험치와 계산치가 잘 일치하여 본 연구에서 제안하는 반응 모델과 속도상수 계산방법이 적절함을 알 수 있었다. 또한 NCO기 90% 전환율에서 allophante/urethane의 비를 계산하였는데 대부분의 조건에서 20% 이상의 높은 값이 얻어져 allophanate 생성반응이 우레탄 물성에 중요한 영향을 미칠 수 있음을 알 수 있었다.