Abstract.
This paper analyzes the cost of extrapolation methods for non-stiff ordinary differential equations depending on the number of digits of accuracy requested. Extrapolation of the explicit midpoint rule is applied for various number sequences. We show that for sequences with arithmetic growth, the cost of the method is polynomial in the number of digits of accuracy, while for sequences of numbers with geometric growth, the cost is super-polynomial with respect to the same parameter.
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Silvana Ilie: Research supported by a postdoctoral fellowship from the Natural Science and Engineering Research Council of Canada.
Robert M. Corless, Chris Essex: Research supported by a grant from the Natural Science and Engineering Research Council of Canada.
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Ilie, S., Corless, R.M. & Essex, C. The Computational Complexity of Extrapolation Methods. Math.Comput.Sci. 2, 557–566 (2009). https://doi.org/10.1007/s11786-007-0040-4
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DOI: https://doi.org/10.1007/s11786-007-0040-4