We consider the application of partitioned Runge-Kutta (PRK) methods to non-autonomous Hamiltonian systems. Necessary and sufficient conditions for the symplecticness of PRK methods are given, more particularly for two low order PRK methods: the partitioned (explicit-implicit) Euler method and the 2-stage Lobatto IIIA-B PRK method. Both methods are often the basis of composition schemes of higher order. In particular for irreducible PRK methods we show the necessity for the nodes of the two underlying PRK methods to be equal.

中文翻译：

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非自治哈密顿系统的一些低阶划分方法的辛性条件

我们考虑将分区Runge-Kutta（PRK）方法应用于非自治哈密顿系统。给出了PRK方法辛的必要性和充分条件，特别是对于两种低阶PRK方法：分区（显式-隐式）欧拉方法和两阶段Lobatto IIIA-B PRK方法。两种方法通常都是高阶合成方案的基础。特别是对于不可约的PRK方法，我们证明了两个基本PRK方法的节点必须相等。