Poisson integrators for Volterra lattice equations

Details Poisson integrators for Volterra lattice equations Poisson integrators for Volterra lattice equations

2005-05-13

arxiv.org/abs/math/0505281v1

Mathematics

Numerical Analysis

9 pages, 2 figures

Scientific paper

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.

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