Abstract
The paper presents explicit interval multistep methods of Milne type, which may be considered as alternative methods to other known explicit interval multistep methods (of Adams-Bashforth and Nyström). It is proved that enclosures of solutions (in the form of intervals) obtained by these methods contain the exact solutions of the initial value problem. Numerical examples show that the widths of intervals obtained by proposed methods are smaller than those obtained by explicit interval multistep methods known so far.
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Acknowledgements
The paper was supported by the Poznan University of Technology (Poland) through the Grants No. 09/91/DSPB/0600 and 02/21/DSPB/3477. This research was also supported in part by PLGrid Infrastructure.
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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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Marciniak, A., Jankowska, M.A. Interval versions of Milne’s multistep methods. Numer Algor 79, 87–105 (2018). https://doi.org/10.1007/s11075-017-0429-3
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DOI: https://doi.org/10.1007/s11075-017-0429-3