Abstract
In this paper, we deal with the differential properties of the scalar flux ϕ ( x ) defined over a two-dimensional bounded convex domain, as a solution to the integral radiation transfer equation. Estimates for the derivatives of ϕ ( x ) near the boundary of the domain are given based on Vainikko’s regularity theorem. The optimal pointwise error estimates in terms of the scalar flux are presented for the two classic finite difference methods: diamond difference (DD) and step difference (SD). Numerical results indicate the implication of the solution smoothness on the numerical convergence behavior.
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