Abstract
Steady-state monoenergetic transport problems for homogeneous domains of large optical thickness τ with smooth scattering functions and sources are considered. The asymptotic approximation to the solution is decomposed into two parts: a regular component and a singular one. Expansions in powers of ε = 1/τ* are constructed for these components on the basis of the boundary layer method and accuracy estimates of asymptotic approximations are established. For slab geometry problems some algorithms are proposed to construct the asymptotic approximation with the singular component exponentially decreasing with moving away from boundaries. Some discrete transport models for these problems are considered and a new approach to construct and investigate coarse-mesh solutions is proposed. It is based on the analysis of the regular and singular components of the mesh solution.
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