Summary
In his fundamental paper on general fixed-stepsize methods, Skeel [6] studied convergence properties, but left the existence of asymptotic expansions as an open problem. In this paper we give a complete answer to this question. For the special cases of one-step and linear multistep methods our proof is shorter than the published ones.
Asymptotic expansions are the theoretical base for extrapolation methods.
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Hairer, E., Lubich, C. Asymptotic expansions of the global error of fixed-stepsize methods. Numer. Math. 45, 345–360 (1984). https://doi.org/10.1007/BF01391413
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DOI: https://doi.org/10.1007/BF01391413