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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
Published electronically: December 1, 2015
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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

Emmanuil Katsoprinakis
Affiliation: Department of Mathematics and Applied Mathematics, University of Crete, 710$$03 Heraklion, Crete, Greece

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.