The Block Arithmetic Mean Iterative Method for Solving Radiation Transport Model

Abstract

This study presents the application of the 2-Point Block Arithmetic Mean (2-BLAM) method for solving radiation transport models formulated as first kind Fredholm integral equations. These equations play a crucial role in predicting radiative heat transfer and neutron or photon transport in slab geometries. The proposed approach used a composite closed Newton-Cotes quadrature scheme to discretize the governing model and formulate a dense algebraic system, which is then solved using the 2-BLAM method. Numerical experiments are carried out on model problems inspired by radiative transfer theory to evaluate the method’s computational efficiency, convergence rate, and solution accuracy. The results demonstrate that 2-BLAM outperforms existing iterative methods in terms of convergence speed and computational cost, highlighting its potential for use in radiation physics applications.