Summary
In this note the geometry of multi-step methods is studied using invariant manifold theory for maps, as familiar from dynamical systems theory. This permits to associate a one-step method to each multi-step method to which the former is not only equivalent asymptotically, but equal in each step if the one-step method is used to produce the initial data of the multi-step method.
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Kirchgraber, U. Multi-step methods are essentially one-step methods. Numer. Math. 48, 85–90 (1986). https://doi.org/10.1007/BF01389443
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DOI: https://doi.org/10.1007/BF01389443