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W. Auzinger, R. Frank, F. Macsek:
"Asymptotic error expansions for stiff equations. Part 2: The mildly stiff case";
Bericht für Technical Report Nr. 68/86, Institut für Angewandte und Numerische Mathematik; 1986.

We derive an asymptotic expansion for the global error of the implicit Euler scheme applied to stiff nonlinear systems of ordinary differential equations. Part 2, in particular, is devoted to the mildly stiff case. It is shown by a discrete singular perturbation analysis of the remainder term equation that the desired order O(h^{q+1}) of the remainder term, which inevitably breaks down at the first grid points, reappears at the subsequent grid points.