Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods

Handle URI:
http://hdl.handle.net/10754/599733
Title:
Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods
Authors:
Hundsdorfer, W.; Mozartova, A.; Spijker, M. N.
Abstract:
In this paper nonlinear monotonicity and boundedness properties are analyzed for linear multistep methods. We focus on methods which satisfy a weaker boundedness condition than strict monotonicity for arbitrary starting values. In this way, many linear multistep methods of practical interest are included in the theory. Moreover, it will be shown that for such methods monotonicity can still be valid with suitable Runge-Kutta starting procedures. Restrictions on the stepsizes are derived that are not only sufficient but also necessary for these boundedness and monotonicity properties. © 2011 Springer Science+Business Media, LLC.
Citation:
Hundsdorfer W, Mozartova A, Spijker MN (2011) Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods. Journal of Scientific Computing 50: 265–286. Available: http://dx.doi.org/10.1007/s10915-011-9487-1.
Publisher:
Springer Nature
Journal:
Journal of Scientific Computing
KAUST Grant Number:
FIC/2010/05
Issue Date:
29-Apr-2011
DOI:
10.1007/s10915-011-9487-1
Type:
Article
ISSN:
0885-7474; 1573-7691
Sponsors:
The work of A. Mozartova is supported by a grant from the Netherlands Organisation for Scientific Research NWO. The work of W. Hundsdorfer for this publication was partially supported by Award No. FIC/2010/05 from King Abdullah University of Science and Technology (KAUST).
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorHundsdorfer, W.en
dc.contributor.authorMozartova, A.en
dc.contributor.authorSpijker, M. N.en
dc.date.accessioned2016-02-28T06:08:34Zen
dc.date.available2016-02-28T06:08:34Zen
dc.date.issued2011-04-29en
dc.identifier.citationHundsdorfer W, Mozartova A, Spijker MN (2011) Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods. Journal of Scientific Computing 50: 265–286. Available: http://dx.doi.org/10.1007/s10915-011-9487-1.en
dc.identifier.issn0885-7474en
dc.identifier.issn1573-7691en
dc.identifier.doi10.1007/s10915-011-9487-1en
dc.identifier.urihttp://hdl.handle.net/10754/599733en
dc.description.abstractIn this paper nonlinear monotonicity and boundedness properties are analyzed for linear multistep methods. We focus on methods which satisfy a weaker boundedness condition than strict monotonicity for arbitrary starting values. In this way, many linear multistep methods of practical interest are included in the theory. Moreover, it will be shown that for such methods monotonicity can still be valid with suitable Runge-Kutta starting procedures. Restrictions on the stepsizes are derived that are not only sufficient but also necessary for these boundedness and monotonicity properties. © 2011 Springer Science+Business Media, LLC.en
dc.description.sponsorshipThe work of A. Mozartova is supported by a grant from the Netherlands Organisation for Scientific Research NWO. The work of W. Hundsdorfer for this publication was partially supported by Award No. FIC/2010/05 from King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Natureen
dc.subjectBoundednessen
dc.subjectInitial value problemen
dc.subjectMethod of lines (MOL)en
dc.subjectMonotonicityen
dc.subjectMultistep methodsen
dc.subjectStrong-stability-preserving (SSP)en
dc.subjectTotal-variation-bounded (TVB)en
dc.subjectTotal-variation-diminishing (TVD)en
dc.titleStepsize Restrictions for Boundedness and Monotonicity of Multistep Methodsen
dc.typeArticleen
dc.identifier.journalJournal of Scientific Computingen
dc.contributor.institutionCentrum voor Wiskunde en Informatica, Amsterdam, Netherlandsen
dc.contributor.institutionLeiden University, Leiden, Netherlandsen
kaust.grant.numberFIC/2010/05en
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