The use of a finite-difference scheme to improve the accuracy of the Modal Expansion Method

The limitation of the Modal Expansion Method for solving the static neutron diffusion equation is demonstrated for cases where the perturbation consists of reactivity device movement. A modification, based on the finite-difference method is applied in regions which contain the reactivity devices. The results show that the error in the calculated reactivity is reduced by a factor between 4 and 10. The error in the maximum bundle and channel power is reduced by a factor of between 1.2 and 6. The computation cost per solution is less than $2.00 on the CDC 6600. The method is useful for analyses that require a relatively large number of approximate solutions to the static neutron diffusion equation