  We consider the multiple scattering of light by fluctuations of the director
in a nematic liquid crystal. Using methods of numerical simulation the peak of
the coherent backscattering and the coefficients of anisotropic diffusion are
calculated. The calculations were carried out without simplifying assumptions
on the properties of the liquid crystal. The process of multiple scattering was
simulated as a random walk of photons in the medium. We investigated in detail
the transition to the diffusion regime. The dependence of the diffusion
coefficients on the applied magnetic field and the wavelength of light were
studied. The results of simulation showed a non-monotonic dependence of the
diffusion coefficients on the external magnetic field. A qualitative
explanation of this behaviour was suggested using a simple scalar model. For
calculation of the peak of the coherent backscattering we used the
semianalytical approach as long as in nematic liquid crystals this peak is
extremely narrow. The parameters of backscattering peak and of diffusion
coefficients which were found in numerical simulations were compared with the
experimental data and the results of analytical calculation.
