  We study the nuclear iso-scalar giant quadruple resonance~(ISGQR) based on
the Boltzmann-Uehling-Uhlenbeck~(BUU) transport equation. The mean-field part
of the BUU equation is described by the Skyrme nucleon-nucleon effective
interaction, and its collision term, which embodies the two-particle-two-hole
($2$p-$2$h) correlation, is implemented through the stochastic approach. We
find that the width of ISGQR for heavy nuclei is exhausted dominated by
collisional damping, which is incorporated into the BUU equation through its
collision term, and it can be well reproduced through employing a proper
in-medium nucleon-nucleon cross section. Based on further Vlasov and BUU
calculations with a number of representative Skyrme interactions, the
iso-scalar nucleon effective mass at saturation density is extracted
respectively as $m^{*}_{s,0}/m$ $=$ $0.83\pm0.04$ and $m^{*}_{s,0}/m$ $=$
$0.82\pm0.03$ from the measured excitation energy $E_x$ of the ISGQR of
$\isotope[208]{Pb}$. The small discrepancy between the two constraints
indicates the negligible role of $2$p-$2$h correlation in constraining
$m_{s,0}^*$ with the ISGQR excitation energy.
