An iterative method for radiative transfer is a slab with specularly reflecting boundary

摘要

The purpose of this paper is to present an iterative scheme for solving the radiative-transfer equation in a scattering, absorbing and emitting slab with specularly reflecting boundary. The medium under consideration is anisotropic, nonhomogeneous and azimuthally unsymmetric, and the boundary surface can be either transparent or reflecting. A novelty of this scheme is that it leads to an explicit recursion formula for the determination of the solution as well as an error estimate for the iterations. The recursion formula involves straightforward integrations of a well-behaved function and can be used to calculate numerical results by using a computer. It is shown that the sequence of iterations from the recursion formula converges uniformly to a unique positive solution of the problem, so that this method also gives an existence and uniqueness theorem.