Even- and odd-parity kinetic equations of particle transport. 1: Algebraic and centered forms of the scattering integral

We consider an equivalent formulation of the linear kinetic transport equation for neutral particles (neutrons, photons) as a system of two equations for even and odd parts of the distribution function. The particle scattering integral of even- and odd-parity transport equations is converted into a non-linear algebraic form and into a centered form. In the algebraic form of the integral we clearly identify the net result of two opposite processes, i.e., particle scattering from a beam and into the beam. In the centered form of the integral the principal terms of scattering processes are canceled out. An iterative method is proposed for the solution of the system of even- and odd-parity equations with these forms of the scattering integral. Convergence of iterations is studied for a one-dimensional plane problem.