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Asymptotic numerical analysis of the diffusion‐discrete absorption equation

The diffusion‐discrete absorption (DDA) equation is considered. This equation contains the standard diffusion term and the discrete sorption expressed by a sum of large number of δ‐functions with the support at a non‐uniform mesh multiplied by the unknown function (concentration). The main result of the paper is the homogenization (continualization) of this equation when the small parameter is the characteristic step h of the mesh. The error estimates are proved for the difference of the exact solution of the DDA equation and the solution of the homogenized differential equation. Copyright © 2012 John Wiley & Sons, Ltd.