  We investigate the performance of various methods of symplectic integration,
which are based on two part splitting of the integration operator, for the
numerical integration of multidimensional Hamiltonian systems. We implement
these schemes to study the behavior of the one-dimensional quartic Klein Gordon
disordered lattice with many degrees of freedom (of the order of a few
hundreds) and compare their efficiency for the weak chaos regime of the
system's dynamics. For this reason we perform extensive simulations for each
considered integration scheme. In the process, the second moment and the
participation number of the propagating wave packets, along with the system's
relative energy error and the required CPU time are registered and compared.
