Bilinear-discontinuous numerical solution of the time dependent transport equation in slab geometry

A bilinear-discontinuous (BLD) discretization in space and time is described for the numerical solution of the discrete ordinates form of the time dependent, one speed neutral particle transport equation in slab geometry. Numerical results using the BLD method are compared with analytical approximations and other space-time discretization schemes. Analysis shows the BLD method is stable and third order accurate in the space and time dimensions independently.