Alternating directions implicit integration in a general linear method framework

dc.contributor.authorSarshar, Arashen
dc.contributor.authorRoberts, Stevenen
dc.contributor.authorSandu, Adrianen
dc.date.accessioned2022-02-27T04:10:17Zen
dc.date.available2022-02-27T04:10:17Zen
dc.date.issued2021-05-15en
dc.date.updated2022-02-27T04:10:16Zen
dc.description.abstractAlternating Directions Implicit (ADI) integration is an operator splitting approach to solve parabolic and elliptic partial differential equations in multiple dimensions based on solving sequentially a set of related one-dimensional equations. Classical ADI methods have order at most two, due to the splitting errors. Moreover, when the time discretization of stiff one-dimensional problems is based on Runge–Kutta schemes, additional order reduction may occur. This work proposes a new ADI approach based on the partitioned General Linear Methods framework. This approach allows the construction of high order ADI methods. Due to their high stage order, the proposed methods can alleviate the order reduction phenomenon seen with other schemes. Numerical experiments are shown to provide further insight into the accuracy, stability, and applicability of these new methods.en
dc.description.versionAccepted versionen
dc.format.extent13 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifierARTN 112619 (Article number)en
dc.identifier.doihttps://doi.org/10.1016/j.cam.2019.112619en
dc.identifier.eissn1879-1778en
dc.identifier.issn0377-0427en
dc.identifier.orcidSandu, Adrian [0000-0002-5380-0103]en
dc.identifier.urihttp://hdl.handle.net/10919/108896en
dc.identifier.volume387en
dc.language.isoenen
dc.publisherElsevieren
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000614702800014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectMathematics, Applieden
dc.subjectMathematicsen
dc.subjectInitial value problemsen
dc.subjectTime integrationen
dc.subjectIMEX methodsen
dc.subjectAlternating directionsen
dc.subjectmath.NAen
dc.subjectcs.NAen
dc.subject65L05, 65L07en
dc.subjectNumerical & Computational Mathematicsen
dc.subject0102 Applied Mathematicsen
dc.subject0103 Numerical and Computational Mathematicsen
dc.subject0906 Electrical and Electronic Engineeringen
dc.titleAlternating directions implicit integration in a general linear method frameworken
dc.title.serialJournal of Computational and Applied Mathematicsen
dc.typeArticleen
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherProceedings Paperen
dc.type.otherMeetingen
dc.type.otherJournalen
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/Engineeringen
pubs.organisational-group/Virginia Tech/Engineering/Computer Scienceen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Engineering/COE T&R Facultyen
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