Abstract
Extrapolation of explicit methods is an interesting approach to solving nonstiff differential equations (see Sect. II.9). Here we show to what extent the idea of extrapolation can also be used for stiff problems. We shall use the results of Sect. I1.8 for the existence of asymptotic expansions and apply them to the study of those implicit and linearly implicit methods, which seem to be most suitable for the computation of stiff differential equations. Our theory here is restricted to classical h → 0 order, the study of stability domains and A -stability.
It seems that a suitable version of an IEM (implicit extrapolation method) which takes care of these difficulties may become a very strong competitor to any of the general discretization methods for stiff systems presently known.
(the very last sentence of Stetter’s book, 1973)
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© 1996 Springer-Verlag Berlin Heidelberg
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Hairer, E., Wanner, G. (1996). Extrapolation Methods. In: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05221-7_9
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DOI: https://doi.org/10.1007/978-3-642-05221-7_9
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