efficient and accurate method for radiation transfer problems

An efficient method of analysis, which utilizes trial functions based on Case's eigenvalues, is developed for solving radiation transfer in an absorbing and scattering homogeneous semi-infinite plane-parallel medium subjected to externally incident radiation. Expressions for the forward and backward intensities, reflectivity and total radiation intensity are included. Numerical results are given and compared involving different forms of the externally incident radiation on the boundary surface. It is shown that the solution converges rapidly to the exact results and that lower-order solutions predict values of the physical parameters that are accurate to five figures in all values of the single-scattering albedos in the range 0.1 ≤ ω ≤ 1. The method has been also used to get approximate formulae for calculating Chandrasekhar's characteristic H-functions and their moments.