Even–odd parity transport equations. 1: Algebraic and centered forms of the scattering source

We consider an equivalent formulation of the linear transport equation of neutral particles (neutrons, photons) as a system of two equations for the even and odd parts of the distribution function. The scattering source of the even-odd parity transport equations is transformed into non-linear algebraic form and into centered form. The algebraic form of the source is constructed from the “net result” of two opposite processes — the escape of particles from the beam and the coming of particles in the beam due to scattering processes. To obtain the centered form, compensation of the main contributions of these opposite processes is performed. We propose the iterative method for solving even-odd parity transport equations with algebraic or centered forms of scattering source. The convergence of the iterations in a plane problem has been studied.