Abstract
A unified error analysis is carried out for two general classes of finite-difference methods for solving discrete-ordinates slab transport equations. Our treatment includes, as special cases, the analysis by E. Larsen and P. Nelson [SIAM J. Numer. Anal., 19 (1982), pp. 334–348] and by B. Neta and H. D. Victory, Jr. [Numer. Funct. Anal. and Optimz., 5(1) (1982), pp. 85–126; SIAM J. Numer. Anal., 20 (1983), pp. 94–105] on several specific finite-difference methods which are linear in nature. In our analysis, we show how the finite-difference approximates at the mesh points can be naturally extended to yield approximates for all values of the spatial variable and obtain a priori estimates of the global discretization errors for these approximates. In addition we show that superconvergence occurs for the (original) finite-difference approximates to the exact discrete-ordinates angular flux at the mesh points and for approximates to several of its spatial moments defined on each mesh cell. We present computati...
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