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Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods. (English) Zbl 1086.65120
Summary: Symplecticity conditions easy to handle for constructing symplectic Runge-Kutta-Nyström methods fitted to trigonometric functions are given. These conditions generalize that of Yu. B. Suris [Zh. Vychisl. Mat. Mat. Fiz. 29, No. 2, 202–211 (1989; Zbl 0686.65039)] when the frequencies tends to zero.
MSC:
65P10Numerical methods for Hamiltonian systems including symplectic integrators
37M15Symplectic integrators (dynamical systems)
65L06Multistep, Runge-Kutta, and extrapolation methods
34A26Geometric methods in differential equations
34A34Nonlinear ODE and systems, general
65L05Initial value problems for ODE (numerical methods)