  We implement several symplectic integrators, which are based on two part
splitting, for studying the chaotic behavior of one- and two-dimensional
disordered Klein-Gordon lattices with many degrees of freedom and investigate
their numerical performance. For this purpose, we perform extensive numerical
simulations by considering many different initial energy excitations and
following the evolution of the created wave packets in the various dynamical
regimes exhibited by these models. We compare the efficiency of the considered
integrators by checking their ability to correctly reproduce several features
of the wave packets propagation, like the characteristics of the created energy
distribution and the time evolution of the systems' maximum Lyapunov exponent
estimator. Among the tested integrators the fourth order $ABA864$ scheme
\cite{BCFLMM13} showed the best performance as it needed the least CPU time for
capturing the correct dynamical behavior of all considered cases when a
moderate accuracy in conserving the systems' total energy value was required.
Among the higher order schemes used to achieve a better accuracy in the energy
conservation, the sixth order scheme $s11ABA82\_6$ exhibited the best
performance.
