Numerical solution of radiative transfer problems in a slab medium by Galerkin-type approximation techniques

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. (orig.)