A new approach of solving the third form of the transport equation in plane geometry: 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.