Numerical method for solving the nonstationary radiation transfer equation in a layered medium

A numerical method for solving an initial-boundary value problem for radiation transfer equation in a layered medium is proposed. The approach is based on sequential use of the Laplace transform and P1-approximation. The use of the Laplace transform allows us to reduce the initial-boundary value problem to a boundary-value problem for a steady-state radiation transfer equation with a parameter. The steady-state problem is convenient for applying the P1-approximation. A numerical implementation of the algorithm and its comparison with Monte Carlo method are performed.