Runge-Kutta methods with minimum storage implementations

Handle URI:
http://hdl.handle.net/10754/561436
Title:
Runge-Kutta methods with minimum storage implementations
Authors:
Ketcheson, David I. ( 0000-0002-1212-126X )
Abstract:
Solution of partial differential equations by the method of lines requires the integration of large numbers of ordinary differential equations (ODEs). In such computations, storage requirements are typically one of the main considerations, especially if a high order ODE solver is required. We investigate Runge-Kutta methods that require only two storage locations per ODE. Existing methods of this type require additional memory if an error estimate or the ability to restart a step is required. We present a new, more general class of methods that provide error estimates and/or the ability to restart a step while still employing the minimum possible number of memory registers. Examples of such methods are found to have good properties. © 2009 Elsevier Inc. All rights reserved.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Numerical Mathematics Group
Publisher:
Elsevier
Journal:
Journal of Computational Physics
Issue Date:
Mar-2010
DOI:
10.1016/j.jcp.2009.11.006
Type:
Article
ISSN:
00219991
Sponsors:
The author thanks Randy LeVeque for the suggestion to consider embedded pairs. This work was funded by a US Dept. of Energy Computational Science Graduate Fellowship.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKetcheson, David I.en
dc.date.accessioned2015-08-02T09:11:16Zen
dc.date.available2015-08-02T09:11:16Zen
dc.date.issued2010-03en
dc.identifier.issn00219991en
dc.identifier.doi10.1016/j.jcp.2009.11.006en
dc.identifier.urihttp://hdl.handle.net/10754/561436en
dc.description.abstractSolution of partial differential equations by the method of lines requires the integration of large numbers of ordinary differential equations (ODEs). In such computations, storage requirements are typically one of the main considerations, especially if a high order ODE solver is required. We investigate Runge-Kutta methods that require only two storage locations per ODE. Existing methods of this type require additional memory if an error estimate or the ability to restart a step is required. We present a new, more general class of methods that provide error estimates and/or the ability to restart a step while still employing the minimum possible number of memory registers. Examples of such methods are found to have good properties. © 2009 Elsevier Inc. All rights reserved.en
dc.description.sponsorshipThe author thanks Randy LeVeque for the suggestion to consider embedded pairs. This work was funded by a US Dept. of Energy Computational Science Graduate Fellowship.en
dc.publisherElsevieren
dc.subjectLow-storageen
dc.subjectMethod of linesen
dc.subjectRunge-Kutta methodsen
dc.titleRunge-Kutta methods with minimum storage implementationsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentNumerical Mathematics Groupen
dc.identifier.journalJournal of Computational Physicsen
kaust.authorKetcheson, David I.en
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