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Rush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology

hal.structure.identifierIHU-LIRYC
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCOUDIÈRE, Yves
hal.structure.identifierIHU-LIRYC
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDOUANLA LONTSI, Charlie
hal.structure.identifierLaboratoire de Mathématiques et de leurs Applications [Pau] [LMAP]
dc.contributor.authorPIERRE, Charles
dc.date.accessioned2024-04-04T03:01:04Z
dc.date.available2024-04-04T03:01:04Z
dc.date.created2018-10-15
dc.date.issued2020-07-14
dc.identifier.issn1068-9613
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192869
dc.description.abstractEnTo address the issues of stability and accuracy for reaction-diffusion equations, the development of high order and stable time-stepping methods is necessary. This is particularly true in the context of cardiac electrophysiology, where reaction-diffusion equations are coupled with stiff ODE systems. Many research have been led in that way in the past 15 years concerning implicit-explicit methods and exponential integrators. In 2009, Perego and Veneziani proposed an innovative time-stepping method of order 2. In this paper we present the extension of this method to the orders 3 and 4 and introduce the Rush-Larsen schemes of order k (shortly denoted RL_k). The RL_k schemes are explicit multistep exponential integrators. They display a simple general formulation and an easy implementation. The RL_k schemes are shown to be stable under perturbation and convergent of order k. Their Dahlquist stability analysis is performed. They have a very large stability domain provided that the stabilizer associated with the method captures well enough the stiff modes of the problem. The RL_k method is numerically studied as applied to the membrane equation in cardiac electrophysiology. The RL k schemes are shown to be stable under perturbation and convergent oforder k. Their Dahlquist stability analysis is performed. They have a very large stability domain provided that the stabilizer associated with the method captures well enough the stiff modes of the problem. The RL k method is numerically studied as applied to the membrane equation in cardiac electrophysiology.
dc.description.sponsorshipModèles numériques haute résolution de l'électrophysiologie cardiaque - ANR-13-MONU-0004
dc.language.isoen
dc.publisherKent State University Library
dc.subject.enexplicit high-order multistep methods
dc.subject.enstiff equations
dc.subject.enstability and convergence
dc.subject.enexponential integrators
dc.subject.enDahlquist stability
dc.title.enRush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
dc.identifier.arxiv1712.02260
bordeaux.journalElectronic Transactions on Numerical Analysis
bordeaux.page342-357
bordeaux.volume55
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01557856
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01557856v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Electronic%20Transactions%20on%20Numerical%20Analysis&rft.date=2020-07-14&rft.volume=55&rft.spage=342-357&rft.epage=342-357&rft.eissn=1068-9613&rft.issn=1068-9613&rft.au=COUDI%C3%88RE,%20Yves&DOUANLA%20LONTSI,%20Charlie&PIERRE,%20Charles&rft.genre=article


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