  An explicit numerical scheme is proposed for solving the initial-boundary
value problem for the radiative transport equation in a rectangular domain with
completely absorbing boundary condition. An upwind finite difference
approximation is applied to the differential terms of the equation, and the
composite trapezoidal rule to the scattering integral. The main results are
positivity, stability, and convergence of the scheme. It is also shown that the
scheme can be regarded as an iterative method for finding numerical solutions
to the stationary transport equation. Some numerical examples for the
two-dimensional problems are given.

Numerical Analysis