A comparative study on classical polynomial approximations to the transport equation in spherical media albedo problems

Abstract

The ultraspherical polynomial approximation which unifies all classical polynomial sequences in a unique form is used to calculate the albedo for isotropic scattering in a homogeneous spherical medium. This is the most general polynomial approach in the sense that it includes all classical polynomial methods to solve the transport equation such as and methods. For the first time an antisymmetric polynomial (ultraspherical polynomial) solution to the corresponding pseudo-slab problem is proposed. Very accurate and consistent albedo values are obtained for a variety of methods when compared to the literature. It is also shown that various approximations differ only in convergency characteristics; some converge monotonically, some in the mean.