Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods

Handle URI:
http://hdl.handle.net/10754/597810
Title:
Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods
Authors:
Mozartova, A.; Savostianov, I.; Hundsdorfer, W.
Abstract:
© 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.
Citation:
Mozartova A, Savostianov I, Hundsdorfer W (2015) Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods. Journal of Computational and Applied Mathematics 279: 159–172. Available: http://dx.doi.org/10.1016/j.cam.2014.10.025.
Publisher:
Elsevier BV
Journal:
Journal of Computational and Applied Mathematics
KAUST Grant Number:
FIC/2010/05
Issue Date:
May-2015
DOI:
10.1016/j.cam.2014.10.025
Type:
Article
ISSN:
0377-0427
Sponsors:
The work of A. Mozartova has been supported by a grant from the Netherlands Organization for Scientific Research NWO. The work of I. Savostianov and W. Hundsdorfer for this publication has been supported by Award No. FIC/2010/05 from the King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorMozartova, A.en
dc.contributor.authorSavostianov, I.en
dc.contributor.authorHundsdorfer, W.en
dc.date.accessioned2016-02-25T12:57:06Zen
dc.date.available2016-02-25T12:57:06Zen
dc.date.issued2015-05en
dc.identifier.citationMozartova A, Savostianov I, Hundsdorfer W (2015) Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods. Journal of Computational and Applied Mathematics 279: 159–172. Available: http://dx.doi.org/10.1016/j.cam.2014.10.025.en
dc.identifier.issn0377-0427en
dc.identifier.doi10.1016/j.cam.2014.10.025en
dc.identifier.urihttp://hdl.handle.net/10754/597810en
dc.description.abstract© 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.en
dc.description.sponsorshipThe work of A. Mozartova has been supported by a grant from the Netherlands Organization for Scientific Research NWO. The work of I. Savostianov and W. Hundsdorfer for this publication has been supported by Award No. FIC/2010/05 from the King Abdullah University of Science and Technology (KAUST).en
dc.publisherElsevier BVen
dc.subjectBoundednessen
dc.subjectInitial value problemen
dc.subjectMethod of lines (MOL)en
dc.subjectMonotonicityen
dc.subjectMultistep methodsen
dc.subjectStrong-stability-preserving (SSP)en
dc.titleComparison of boundedness and monotonicity properties of one-leg and linear multistep methodsen
dc.typeArticleen
dc.identifier.journalJournal of Computational and Applied Mathematicsen
dc.contributor.institutionCentrum voor Wiskunde en Informatica, Amsterdam, Netherlandsen
kaust.grant.numberFIC/2010/05en
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