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Backward difference formulae: New multipliers and stability properties for parabolic equations


Authors: Georgios Akrivis and Emmanuil Katsoprinakis
Journal: Math. Comp. 85 (2016), 2195-2216
MSC (2010): Primary 65M12, 65M60; Secondary 65L06
DOI: https://doi.org/10.1090/mcom3055
Published electronically: December 1, 2015
MathSciNet review: 3511279
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Abstract: We determine new, more favorable, and in a sense optimal, multipliers for the three- and five-step backward difference formula (BDF) methods. We apply the new multipliers to establish stability of these methods as well as of their implicit–explicit counterparts for parabolic equations by energy techniques, under milder conditions than the ones recently imposed in [1, 4].


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Additional Information

Georgios Akrivis
Affiliation: Department of Computer Science & Engineering, University of Ioannina, 451$\,$10 Ioannina, Greece
MR Author ID: 24080
Email: akrivis@cs.uoi.gr

Emmanuil Katsoprinakis
Affiliation: Department of Mathematics and Applied Mathematics, University of Crete, 710$\,$03 Heraklion, Crete, Greece
Email: katsopr@uoc.gr

Keywords: BDF methods, multipliers, implicit–explicit BDF methods, parabolic equations, stability, energy technique
Received by editor(s): July 30, 2014
Received by editor(s) in revised form: February 25, 2015, and March 12, 2015
Published electronically: December 1, 2015
Additional Notes: The work of the first author was partially supported by GSRT-ESET “Excellence” grant 1456.
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.