There is currently much interest in developing new codes and improving the existing ones to be able to predict instabilities of nuclear power reactors. Stability calculations are very sensitive to the models used for the reactor and the numerical methods used to integrate them. To clarify this dependence, a simplified thermohydraulic model has been proposed, and several numerical schemes have been used to integrate the model. A numerical example has been analyzed showing that the behavior of the solution depends mainly on the spatial discretization used.