Convergence of the Modified Discrete Ordinates Method for the Anisotropic Scattering Transport Equation

Criticality problem of nuclear tractors generally refers to an eigenvalue problem for the transport equations. In this paper, we deal with the eigenvalue of the anisotropic scattering transport equation in slab geometry. We propose a new discrete method which was called modified discrete ordinates method. It is constructed by redeveloping and improving discrete ordinates method in the space of L1(X). Different from traditional methods, norm convergence of operator approximation is proved theoretically. Furthermore, convergence of eigenvalue approximation and the corresponding error estimation are obtained by analytical tools.