  We review the recent progress on studying the nuclear collective dynamics by
solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation with the lattice
Hamiltonian method treating the collision term by the full-ensemble stochastic
collision approach. This lattice BUU (LBUU) method has recently been developed
and implemented in a GPU parallel computing technique, and achieves a rather
stable nuclear ground-state evolution and high accuracy in evaluating the
nucleon-nucleon (NN) collision term. This new LBUU method has been applied to
investigate the nuclear isoscalar giant monopole resonances and isovector giant
dipole resonances. While the calculations with the LBUU method without the NN
collision term (i.e., the lattice Hamiltonian Vlasov method) describe
reasonably the excitation energies of nuclear giant resonances, the full LBUU
calculations can well reproduce the width of the giant dipole resonance of
$^{208}$Pb by including a collisional damping from NN scattering. The observed
strong correlation between the width of nuclear giant dipole resonance and the
NN elastic cross section suggests that the NN elastic scattering plays an
important role in nuclear collective dynamics, and the width of nuclear giant
dipole resonance provides a good probe of the in-medium NN elastic cross
section.
