The singular eigenfunction analysis of the third form transport equation using half-range orthogonality relations: the half-space problems

Abstract

The third form transport equation is solved using the infinite medium Green's functions in terms of the singular eigenfunctions of the method of elementary solutions and their half-range orthogonality relations. For simplicity, we consider only the Fredholm equation of the first kind and obtain the solution of the two problems for isotropic scattering: (i) the albedo problem for a source free half-space and (ii) the extrapolation length for the Milne problem. The convergence of the numerical results is fast as in C N method and the analytical expressions are simple for solving numerically.