Pointwise Convergence of the Three-Dimensional Discrete Ordinate Method

The discrete ordinate method is a numerical technique used for obtaining approximate solutions to the transport equation. The approximate solutions are shown to converge pointwise to the exact solution, provided: (a) that the average number of secondary neutrons produced per collisionis less than unity; (b) that the truncation error in the quadrature formula used vanishes as the number of discrete ordinates used tends to infinity.