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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:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
70-08 Computational methods for problems pertaining to mechanics of particles and systems

Citations:

Zbl 0785.65083
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Full Text: DOI

References:

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