  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.
