Poisson integrators for Volterra lattice equations

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Ergenc T., Karasozen B.

APPLIED NUMERICAL MATHEMATICS, vol.56, no.6, pp.879-887, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 6
  • Publication Date: 2006
  • Doi Number: 10.1016/j.apnum.2005.06.009
  • Journal Name: APPLIED NUMERICAL MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.879-887
  • Keywords: Volterra lattice equations, Korteweg-de Vries equation, Bi-Hamiltonian systems, Poisson structure, Lobatto methods, symplectic Euler method, LOTKA-VOLTERRA, SYSTEM
  • Middle East Technical University Affiliated: Yes

Abstract

The Volterra lattice equations are completely integrable and possess bi-Hamiltonian structure. They are integrated using partitioned Lobatto IIIA-B methods which preserve the Poisson structure. Modified equations are derived for the symplectic Euler and second order Lobatto IIIA-B method. Numerical results confirm preservation of the corresponding Hamiltonians, Casimirs, quadratic and cubic integrals in the long-term with different orders of accuracy. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.