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Article: On a parabolic sine-gordon model

TitleOn a parabolic sine-gordon model
Authors
KeywordsBackward differentiation formula
Implicit-explicit scheme
Sine-Gordon equation
Issue Date2021
Citation
Numerical Mathematics, 2021, v. 14, n. 4, p. 1068-1084 How to Cite?
AbstractWe consider a parabolic sine-Gordon model with periodic boundary conditions. We prove a fundamental maximum principle which gives a priori uniform control of the solution. In the one-dimensional case we classify all bounded steady states and exhibit some explicit solutions. For the numerical discretization we employ first order IMEX, and second order BDF2 discretization without any additional stabilization term. We rigorously prove the energy stability of the numerical schemes under nearly sharp and quite mild time step constraints. We demonstrate the striking similarity of the parabolic sine-Gordon model with the standard Allen-Cahn equations with double well potentials.
Persistent Identifierhttp://hdl.handle.net/10722/327359
ISSN
2023 Impact Factor: 1.9
2023 SCImago Journal Rankings: 0.670
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorCheng, Xinyu-
dc.contributor.authorLi, Dong-
dc.contributor.authorQuan, Chaoyu-
dc.contributor.authorYang, Wen-
dc.date.accessioned2023-03-31T05:30:46Z-
dc.date.available2023-03-31T05:30:46Z-
dc.date.issued2021-
dc.identifier.citationNumerical Mathematics, 2021, v. 14, n. 4, p. 1068-1084-
dc.identifier.issn1004-8979-
dc.identifier.urihttp://hdl.handle.net/10722/327359-
dc.description.abstractWe consider a parabolic sine-Gordon model with periodic boundary conditions. We prove a fundamental maximum principle which gives a priori uniform control of the solution. In the one-dimensional case we classify all bounded steady states and exhibit some explicit solutions. For the numerical discretization we employ first order IMEX, and second order BDF2 discretization without any additional stabilization term. We rigorously prove the energy stability of the numerical schemes under nearly sharp and quite mild time step constraints. We demonstrate the striking similarity of the parabolic sine-Gordon model with the standard Allen-Cahn equations with double well potentials.-
dc.languageeng-
dc.relation.ispartofNumerical Mathematics-
dc.subjectBackward differentiation formula-
dc.subjectImplicit-explicit scheme-
dc.subjectSine-Gordon equation-
dc.titleOn a parabolic sine-gordon model-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.4208/NMTMA.OA-2021-0040-
dc.identifier.scopuseid_2-s2.0-85115777547-
dc.identifier.volume14-
dc.identifier.issue4-
dc.identifier.spage1068-
dc.identifier.epage1084-
dc.identifier.eissn2079-7338-
dc.identifier.isiWOS:000695218700010-

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