Numerical Solution of Radiative Transfer Problems in a Slab Medium by Galerkin-type Approximation Techniques

Abstract

An approximate method for solving the radiative transfer equation in a slab medium with an isotropic scattering is proposed. The method is based upon constructing the double Legendre series to approximate the required solution using a Galerkin-type method. The differential and integral expressions which arise in the radiative transfer equation are converted into a system of linear algebraic equations which can be solved for the unknown coefficients. Numerical examples are included to demonstrate the validity and applicability of the method and a comparison is made with existing results.

The meshless method for solving radiative transfer problems in a slab medium based on radial basis functions

“…where c i are the expansion coefficients with c 0 = 1. The RTE in slab medium with anisotropic scattering has some numerical and rigorous solutions such as: two-flux [4,5], spherical harmonic [6,7], series expansion [8,9,10], integral equation [11,12], Padé approximation [13], iterative [6], variational [11,14,15], eigenfunction expansion [16,17], the linear spline approximation [1], the generalized Eddington approximation [3] and Spectral methods approximation [18,19,20].…”