Weighted Central Difference Equations for the Neutron Transport Equation

A family of centered difference methods for approximating the solution of the neutron transport equation in x-y geometry is considered. Positivity of some of the difference methods is shown for sufficiently small mesh spacings. Also, in general, the weighted central difference schemes appear to be less oscillatory than the standard diamond scheme. Numerical results as well as heuristic arguments to support these conclusions are presented.