Displaying similar documents to “On order 5 symplectic explicit Runge-Kutta Nyström methods.”

On energy conservation of the simplified Takahashi-Imada method

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...

Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs

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 y ' ' = f x , y 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...