Iterative schemes for the neutron diffusion equation

We study iterative methods for solving linear systems arising in the discretization of the time dependent neutron diffusion equation. These methods are obtained accelerating two different stationary iterative methods, of second degree type, with a variational technique. We have obtained some results concerning the convergence and the selection of the optimal extrapolation factor for some particular matrices. To test their performance, the bidimensional seed-blanket transient has been simulated. From the numerical results, compared with the ones obtained with other methods as the restarted GMRES, BiCGSTAB, and TFQMR, we can conclude that the proposed methods are competitive for this type of problem.