Application of the collocation method to the solution of the time-dependent neutron diffusion equation

In the past several years, with the development of the coarse-mesh schemes for the spatial discretization of the diffusion equations, the computing time for the static neutron flux calculations has been reduced considerably over the conventional finite difference scheme. For the temporal discretization in the time-dependent case, a fully implicit method (FIM) was found to be more efficient than either the explicit or the alternating-direction explicit method. In this paper, a new approach using the collocation method is investigated for the temporal discretization in an effort to further improve the computing time over that of the FIM