A New Approach to Solving the Third form of the Transport Equation in Plane Geometry: the Half-space Albedo Problem

Abstract

In a new approach of solving the third form of the transport equation, one should consider and compare the two methods C_N and F_N. Both of the methods depend on the use of Green's function. In C_N method the Green's function obtained by the Fourier-transform technique is used to solve the system of integral equations which is provided at the boundary of the various media. In F_N method which is a modified version of C_N method, The Green's function in terms of singular eigenfunctions is used to solve the integro-differential form of the Boltzmann equation. In our approach we use the Green's function of F_N method to solve C_N equations. That is Green's function in terms of singular eigenfunctions is used to solve the system of integral equations of C_N method. As in F_N method this approach yields simple analytical equations that can be solved numericaly even more efficiently than the C_N method and the convergence of the numerical results is faster than the numerical results of F_N method.