An overview of Hamiltonian systems with noncanonical Poisson structures is given. Examples of bi-Hamiltonian ODEs, PDEs, and lattice equations are presented. Numerical integrators using generating functions, Hamiltonian splitting, symplectic Runge-Kutta methods are discussed for Lie-Poisson systems and Hamiltonian systems with a general Poisson structure. Nambu-Poisson systems and the discrete gradient methods are also presented. © 2005 Elsevier Ltd. All rights reserved.
Karasözen, B. (2004). Poisson integrators. Mathematical and Computer Modelling, 40(11–12), 1225–1244. https://doi.org/10.1016/j.mcm.2005.01.015