Discrete-analytical difference scheme for solving the nonstationary particle transport equation by the splitting method

A discrete-analytical difference scheme is presented for solving the nonstationary kinetic particle (neutron) transport equation in the multigroup isotropic approximation by applying the splitting method. A feature of the scheme is that the solution of the transport equation in the multigroup model is reduced to solving equations in the one-group model. The efficiency of the scheme is ensured by computing the collision integral with the use of analytical solutions of ordinary differential equations describing the evolution of neutrons arriving at the group g from all groups $g'$. Solutions of the equations are found without using iteration with respect to the collision integral or matrix inversion. The solution method can naturally be generalized to problems in multidimensional spaces and can be parallelized.