  We develop a new lattice Hamiltonian method for solving the
Boltzmann-Uehling-Uhlenbeck (BUU) equation. Adopting the stochastic approach to
treat the collision term and using the GPU parallel computing to carry out the
calculations allows for a rather high accuracy in evaluating the collision
term, especially its Pauli blocking, leading thus to a new level of precision
in solving the BUU equation. Applying this lattice BUU method to study the
width of giant dipole resonance (GDR) in nuclei, where the accurate treatment
of the collision term is crucial, we find that the obtained GDR width of
$^{208}{\rm Pb}$ shows a strong dependence on the in-medium nucleon-nucleon
cross section $\sigma_{\rm NN}^*$. A very large medium reduction of
$\sigma_{\rm NN}^*$ is needed to reproduce the measured value of the GDR width
of $^{208}{\rm Pb}$ at the Research Center for Nuclear Physics in Osaka, Japan.
