  In this paper, we first present a multiple-relaxation-time lattice Boltzmann
(MRT-LB) model for one-dimensional diffusion equation where the D1Q3 (three
discrete velocities in one-dimensional space) lattice structure is considered.
Then through the theoretical analysis, we derive an explicit four-level
finite-difference scheme from this MRT-LB model. The results show that the
four-level finite-difference scheme is unconditionally stable, and through
adjusting the weight coefficient $\omega_{0}$ and the relaxation parameters
$s_1$ and $s_2$ corresponding to the first and second moments, it can also have
a sixth-order accuracy in space. Finally, we also test the four-level
finite-difference scheme through some numerical simulations, and find that the
numerical results are consistent with our theoretical analysis.
