Abstract
This chapter presents the numerical analysis of the neutron transport equation. It reviews some regularity results for solutions of the transport equation, and discusses some numerical methods for solving the equation. The solutions of the transport equation display singularities, even in the simplest situations. In practical multidimensional problems, the presence of material interfaces gives rise to further singularities in the solution of transport problems. As an example of this, the transport equation is considered in a plane polygonal region R , with isotropic scattering and isotropic source. The chapter presents an assumption that that R is divided into a number of polygonal subregions Ri and that in each subregion the coefficients of the equation are constant. It also discusses two methods for discretizing the angular variable in transport problems: (1) the spherical harmonics method and (2) the discrete ordinate method. If the Galerkin method is applied in the context of Vladimirov's self-adjoint formulation of the transport equation, the spherical harmonics approximation emerges as the best possible approximation in a certain sense.
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