State-dependent symplecticity and area preserving numerical methods
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摘要
We introduce the definition of state-dependent symplecticity as a useful tool of investigation to discover nearby symplecticity in symmetric non-symplectic one-step methods applied to two-dimensional Hamiltonian systems. We first relate this property to Poisson systems and to the trapezoidal method, and then investigate Runge–Kutta and discrete gradient symmetric methods.
论文关键词：65L05,65P10,37M15,Hamiltonian systems,Poisson systems,Symplecticity,Runge–Kutta methods,Discrete gradient methods
论文评审过程：Received 28 July 2005, Available online 24 July 2006.
论文官网地址：https://doi.org/10.1016/j.cam.2006.02.058
