An Optimal Choice of the Initial Flux for Iterative Solutions of the Inhomogeneous Transport Equation

We study the dependence of the number, N, of iterations necessary for the convergence of the one-group inhomogeneous transport equation, on the normalization, α, of an initial flux proportional to the external source distribution. It is proven that if the initial flux has the correct ψ₀ component, where ψ₀ is the fundamental eigenfunction of the corresponding homogeneous equation, the number of iterations is significantly reduced. This minimum is already indicated by a heuristic neutron-balance argument, whereas the complete function N(α) is derived by means of a rigorous analysis. Results of this analysis are illustrated by some numerical examples.