Poisson integrators for Volterra lattice equations

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Ergenc T., Karasozen B.

APPLIED NUMERICAL MATHEMATICS, cilt.56, sa.6, ss.879-887, 2006 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 56 Sayı: 6
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/j.apnum.2005.06.009
  • Dergi Adı: APPLIED NUMERICAL MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.879-887
  • Anahtar Kelimeler: Volterra lattice equations, Korteweg-de Vries equation, Bi-Hamiltonian systems, Poisson structure, Lobatto methods, symplectic Euler method, LOTKA-VOLTERRA, SYSTEM
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.