A method of the convergence acceleration in transport theory problems

A certain numerical procedures of boundary problem solutions in the neutron transport theory problems for the case of media with the piecewise-constant spatial dependence of the cross-section are considered. These procedures are a combination of the simple iteration method and projection method, in which the coordinate functions are chosen as a certain superimpositions of elementary solutions of the corresponding homogeneous transport equations. Such a choice results in good solutions in already the lowest order iterations of the properly modified simple iteration procedure