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

dc.contributor.authorMozartova, A.
dc.contributor.authorSavostianov, I.
dc.contributor.authorHundsdorfer, W.
dc.contributor.institutionCentrum voor Wiskunde en Informatica, Amsterdam, Netherlands
dc.date.accessioned2016-02-25T12:57:06Z
dc.date.available2016-02-25T12:57:06Z
dc.date.issued2015-05
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.
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).
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.
dc.identifier.doi10.1016/j.cam.2014.10.025
dc.identifier.issn0377-0427
dc.identifier.journalJournal of Computational and Applied Mathematics
dc.identifier.urihttp://hdl.handle.net/10754/597810
dc.publisherElsevier BV
dc.subjectBoundedness
dc.subjectInitial value problem
dc.subjectMethod of lines (MOL)
dc.subjectMonotonicity
dc.subjectMultistep methods
dc.subjectStrong-stability-preserving (SSP)
dc.titleComparison of boundedness and monotonicity properties of one-leg and linear multistep methods
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Mozartova, A.,equals">Mozartova, A.</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Savostianov, I.,equals">Savostianov, I.</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Hundsdorfer, W.,equals">Hundsdorfer, W.</a><br><br><h5>KAUST Grant Number</h5>FIC/2010/05<br><br><h5>Date</h5>2015-05</span>
display.details.right<span><h5>Abstract</h5>© 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.<br><br><h5>Citation</h5>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.<br><br><h5>Acknowledgements</h5>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).<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Elsevier BV,equals">Elsevier BV</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Journal of Computational and Applied Mathematics,equals">Journal of Computational and Applied Mathematics</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1016/j.cam.2014.10.025">10.1016/j.cam.2014.10.025</a></span>
kaust.grant.numberFIC/2010/05
orcid.authorMozartova, A.
orcid.authorSavostianov, I.
orcid.authorHundsdorfer, W.
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