Poisson integrators

Details Poisson integrators Poisson integrators

2005-05-13

arxiv.org/abs/nlin/0505037v1

Mathematical and Computer Modelling 40 (2004) 1225-1244

Nonlinear Sciences

Exactly Solvable and Integrable Systems

30 pages

Scientific paper

An overview of Hamiltonian systems with noncanonical Poisson structures is given. Examples of bi-Hamiltonian ode's, pde's 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.

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