The CN method applied to the stationary problem of particle reflection by a purely scattering or weakly absorbing half-space; extension to the asymptotic time-dependent case

The application of the classical CN method fails for a pure scattering or weakly absorbing medium. The asymptotic CN method, in stationary mode, is the way to solve the transport equation in this limiting case, when c is equal or very close to 1. The asymptotic method allows us to obtain the asymptotic time-dependent emergent angular distribution for a given impinging angular intensity at t = 0 whatever c may be. The numerical results for the classical and asymptotic methods are consistent in the overlapping range.