Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size

Handle URI:
http://hdl.handle.net/10754/621858
Title:
Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size
Authors:
Hadjimichael, Yiannis ( 0000-0003-3517-8557 ) ; Ketcheson, David I. ( 0000-0002-1212-126X ) ; Loczi, Lajos ( 0000-0002-7999-5658 ) ; Németh, Adrián
Abstract:
Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order two and three) with variable step size, and prove their optimality, stability, and convergence. The choice of step size for multistep SSP methods is an interesting problem because the allowable step size depends on the SSP coefficient, which in turn depends on the chosen step sizes. The description of the methods includes an optimal step-size strategy. We prove sharp upper bounds on the allowable step size for explicit SSP linear multistep methods and show the existence of methods with arbitrarily high order of accuracy. The effectiveness of the methods is demonstrated through numerical examples.
KAUST Department:
Computer, Electrical, and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Jeddah 23955-6900, Saudi Arabia
Citation:
Hadjimichael Y, Ketcheson DI, Lóczi L, Németh A (2016) Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size. SIAM Journal on Numerical Analysis 54: 2799–2832. Available: http://dx.doi.org/10.1137/15M101717X.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Numerical Analysis
Issue Date:
8-Sep-2016
DOI:
10.1137/15M101717X
Type:
Article
ISSN:
0036-1429; 1095-7170
Sponsors:
This work was supported by the King Abdullah University of Science and Technology (KAUST), 4700 Thuwal, 23955-6900, Saudi Arabia. The work of the fourth author was partially supported by the grant TAMOP-4.2.2.A-11/1/KONV-2012-0012.
Additional Links:
http://epubs.siam.org/doi/10.1137/15M101717X
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorHadjimichael, Yiannisen
dc.contributor.authorKetcheson, David I.en
dc.contributor.authorLoczi, Lajosen
dc.contributor.authorNémeth, Adriánen
dc.date.accessioned2016-11-22T08:50:25Z-
dc.date.available2016-11-22T08:50:25Z-
dc.date.issued2016-09-08en
dc.identifier.citationHadjimichael Y, Ketcheson DI, Lóczi L, Németh A (2016) Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size. SIAM Journal on Numerical Analysis 54: 2799–2832. Available: http://dx.doi.org/10.1137/15M101717X.en
dc.identifier.issn0036-1429en
dc.identifier.issn1095-7170en
dc.identifier.doi10.1137/15M101717Xen
dc.identifier.urihttp://hdl.handle.net/10754/621858-
dc.description.abstractStrong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order two and three) with variable step size, and prove their optimality, stability, and convergence. The choice of step size for multistep SSP methods is an interesting problem because the allowable step size depends on the SSP coefficient, which in turn depends on the chosen step sizes. The description of the methods includes an optimal step-size strategy. We prove sharp upper bounds on the allowable step size for explicit SSP linear multistep methods and show the existence of methods with arbitrarily high order of accuracy. The effectiveness of the methods is demonstrated through numerical examples.en
dc.description.sponsorshipThis work was supported by the King Abdullah University of Science and Technology (KAUST), 4700 Thuwal, 23955-6900, Saudi Arabia. The work of the fourth author was partially supported by the grant TAMOP-4.2.2.A-11/1/KONV-2012-0012.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/15M101717Xen
dc.rightsArchived with thanks to SIAM Journal on Numerical Analysisen
dc.subjectstrong stability preservationen
dc.subjectmonotonicityen
dc.subjectlinear multistep methodsen
dc.subjectvariable step sizeen
dc.subjecttime integrationen
dc.titleStrong Stability Preserving Explicit Linear Multistep Methods with Variable Step Sizeen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical, and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Jeddah 23955-6900, Saudi Arabiaen
dc.identifier.journalSIAM Journal on Numerical Analysisen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionSzechenyi Istvan University, Gyor, H-9026, Hungaryen
kaust.authorHadjimichael, Yiannisen
kaust.authorKetcheson, David I.en
kaust.authorLoczi, Lajosen
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