Poisson流形上广义Hamilton系统的保结构算法

An Algorithm for Preserving the Generalized Poisson Bracket Structure of Generalized Hamiltonian System

Poisson流形是研究广义 Hamilton系统的恰当几何结构。本文在 Poisson流形上讨论广义Hamilton系统的保结构的数值解法 ,为广义 Hamilton系统的数值计算提供了理论基础。文中通过算例证明了算法的保结构性和稳定性 ,同时说明了该算法可以推广到广义 Hamilton控制系统。

Feng, in Ref. 2, proposed an algorithm for preserving the canonical character of Hamiltonian system, thus ensuring that numerical iteration lead to correct results. We propose an algorithm for preserving the canonical character of generalized Hamiltonian system. We preserve its canonical character by preserving its generalized Poisson bracket structure. Section 2 mentions the research results of Ref. 4 on conditions that must be strictly observed for preserving generalized Poisson bracket structure. Section 3 gives our algorithm, which is an explicit scheme of second order, and discusses how we introduce embedding cycle in our algorithm to make its precision higher. Section 4 gives a numerical example and the numerical results given in Table 1 show preliminarily that our algorithm is feasible.