An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit

An asymptotic-induced scheme for nonstationary transport equations with the diffusion scaling is developed. The scheme works uniformly for all ranges of mean-free paths. It is based on the asymptotic analysis of the diffusion limit of the transport equation. A theoretical investigation of the behavior of the scheme in the diffusion limit is given and an approximation property is proven. Moreover, numerical results for different physical situations are shown and the uniform convergence of the scheme is established numerically.

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