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A symplectic Runge-Kutta-Nyström method with minimal phase-lag. (English) Zbl 1209.65075
Summary: We introduce a symplectic explicit RKN method for Hamiltonian systems with periodical solutions. The method has algebraic order three and phase-lag order six at a cost of three function evaluations per step. Numerical experiments show the relevance of the developed algorithm. It is found that the new method is much more efficient than the standard symplectic fourth-order method [M.P. Calvo, J.M. Sanz-Serna, SIAM J. Sci. Comput. 14, No. 4, 936–952 (1993; Zbl 0785.65083)].
MSC:
65L06Multistep, Runge-Kutta, and extrapolation methods
37M15Symplectic integrators (dynamical systems)
70-08Computational methods (mechanics of particles and systems)