• Korean Journal of Mathematics
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• v.21 no.3
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• pp.271-283
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• 2013

In this paper, a generalized Adams-Moulton method that is a $m$-step method derived by using the Taylor's series is proposed to solve the satellite orbit determination problem. We show that our proposed method has produced much smaller error than the original Adams-Moulton method. Finally, the accuracy performance is demonstrated in the satellite orbit correction problem by giving a numerical example.

• Journal of Korean Association for Spatial Structures
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• v.18 no.3
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• pp.83-91
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• 2018

In this study, we investigated the dynamic stability of the system and the semi-analytical solution of the shallow arch. The governing equation for the primary symmetric mode of the arch under external load was derived and expressed simply by using parameters. The semi-analytical solution of the equation was obtained using the Taylor series and the stability of the system for the constant load was analyzed. As a result, we can classify equilibrium points by root of equilibrium equation, and classified stable, asymptotical stable and unstable resigns of equilibrium path. We observed stable points and attractors that appeared differently depending on the shape parameter h, and we can see the points where dynamic buckling occurs. Dynamic buckling of arches with initial condition did not occur in low shape parameter, and sensitive range of critical boundary was observed in low damping constants.

• 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.