  In this paper, based on the previous work [B. Shi, Z. Guo, Lattice Boltzmann
model for nonlinear convection-diffusion equations, Phys. Rev. E 79 (2009)
016701], we develop a general multiple-relaxation-time (MRT) lattice Boltzmann
model for nonlinear anisotropic convection-diffusion equation (NACDE), and show
that the NACDE can be recovered correctly from the present model through the
Chapman-Enskog analysis. We then test the MRT model through some classic CDEs,
and find that the numerical results are in good agreement with analytical
solutions or some available results. Besides, the numerical results also show
that similar to the single-relaxation-time (SRT) lattice Boltzmann model or
so-called BGK model, the present MRT model also has a second-order convergence
rate in space. Finally, we also perform a comparative study on the accuracy and
stability of the MRT model and BGK model by using two examples. In terms of the
accuracy, both the theoretical analysis and numerical results show that a
\emph{numerical} slip on the boundary would be caused in the BGK model, and
cannot be eliminated unless the relaxation parameter is fixed to be a special
value, while the \emph{numerical} slip in the MRT model can be overcome once
the relaxation parameters satisfy some constrains. The results in terms of
stability also demonstrate that the MRT model could be more stable than the BGK
model through tuning the free relaxation parameters.
