High order explicit Runge-Kutta pairs for ephemerides of the solar system and the Moon.
Sharp, Philip W. (2000)
Journal of Applied Mathematics and Decision Sciences
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Sharp, Philip W. (2000)
Journal of Applied Mathematics and Decision Sciences
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H.J. Pesch, S. Miesbach (1992)
Numerische Mathematik
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Görtz, Peter, Scherer, Rudolf (1994)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
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Truong Nguyen-Ba, Vladan Božić, Emmanuel Kengne, Rémi Vaillancourt (2009)
Publications de l'Institut Mathématique
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Ernst Hairer, Robert I. McLachlan, Robert D. Skeel (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
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In long-time numerical integration of Hamiltonian systems, and especially in molecular dynamics simulation, it is important that the energy is well conserved. For symplectic integrators applied with sufficiently small step size, this is guaranteed by the existence of a modified Hamiltonian that is exactly conserved up to exponentially small terms. This article is concerned with the simplified Takahashi-Imada method, which is a modification of the Störmer-Verlet method that is as easy...
S. O. Imoni, M. N. O. Ikhile (2014)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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For initial value problem (IVPs) in ordinary second order differential equations of the special form possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem...
Senu, Norazak, Suleiman, Mohamed, Ismail, Fudziah, Othman, Mohamed (2010)
Mathematical Problems in Engineering
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