Moment method is used to obtain space discretizations for discrete ordinates transport equations in slab geometry. Legendre polynomials relating to the space cell are considered as the base functions. The system of N + 1 balance equations (N ≥ 0) for each cell is supplemented by a closing relation of continuous moment method, connecting N+1 solution space moments with cell edge values. The unique solvability of mesh equations is proved. Estimations of mesh solutions are established. Their accuracy is investigated for optically small sells (∑_tΔ < 1). The superconvergence of edge cell and cell average values is established for arbitrary N: passage to the following   approximation   (N → N+1)   improves   the error   estimation   on   two   orders: 0[(∑_tΔ)^2N+2] → 0[(∑_tΔ)^2N+4]. A new approach to construct and investigate coarse mesh solutions is proposed. It is based on the analysis of the mesh solution regular and singular components.

Mathematical problems and theory of numerical methods

Germogenova T. A.,  KIAM RAS