Acceleration of iterations when solving the particle transport equation by extrapolating the source by iteration index

The rate of convergence of the iterative algorithm for solving the transport equation of particles (neutrons or photons) is investigated. The iteration acceleration algorithm is based on nonlinear extrapolation of the source of scattered particles by the iteration index. A series of test problems was solved. It was found that the acceleration coefficient increases with increasing the problem degeneration (i.e., with increasing the ratio of the conservative scattering cross section of particles to the total cross section) and reaches a value of ten. The combination of the method with the Seidel method additionally increases the acceleration coefficient by one and a half to two times. The advantages of the method are simplicity of implementation, a small number of arithmetic operations and a small amount of stored information during the iteration. The method is comparable to the method of simple iterations on these parameters.