Poisson integrators


Karasozen B.

MATHEMATICAL AND COMPUTER MODELLING, vol.40, pp.1225-1244, 2004 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40
  • Publication Date: 2004
  • Doi Number: 10.1016/j.mcm.2005.01.015
  • Title of Journal : MATHEMATICAL AND COMPUTER MODELLING
  • Page Numbers: pp.1225-1244
  • Keywords: Hamiltonian ODEs and PDEs, symplectic integrators, Lie-Poisson systems, Bi-Hamiltonian systems, integrable discretizations, Nambu-Hamiltonian systems, NONLINEAR SCHRODINGER-EQUATION, GENERALIZED NAMBU MECHANICS, KUTTA COLLOCATION METHODS, BI-HAMILTONIAN SYSTEMS, SYMPLECTIC INTEGRATORS, GEOMETRIC INTEGRATORS, DISCRETIZATIONS, MANIFOLDS, SCHEMES, CONSTRUCTION

Abstract

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. (C) 2005 Elsevier Ltd. All rights reserved.