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Exponential Adams Bashforth integrators for stiff ODEs, application to cardiac electrophysiology

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
dc.contributor.authorCOUDIÈRE, Yves
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
dc.contributor.authorDOUANLA LONTSI, Charlie
hal.structure.identifierLaboratoire de Mathématiques et de leurs Applications [Pau] [LMAP]
dc.contributor.authorPIERRE, Charles
dc.date.accessioned2024-04-04T03:06:11Z
dc.date.available2024-04-04T03:06:11Z
dc.date.created2018-04-16
dc.date.issued2018
dc.identifier.issn0378-4754
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193315
dc.description.abstractEnModels in cardiac electrophysiology are coupled systems of reaction diffusion PDE and of ODE. The ODE system displays a very stiff behavior. It is non linear and its upgrade at each time step is a preponderant load in the computational cost. The issue is to develop high order explicit and stable methods to cope with this situation.In this article, is is analyzed the resort to exponential Adams Bashforth (EAB) integrators in cardiac electrophysiology. The method is presented in the framework of a general and varying stabilizer, that is well suited in this context. Stability under perturbation (or 0-stability) is proven. It provides a new approach for the convergence analysis of the method. The Dahlquist stability properties of the method is performed. It is presented in a new framework that incorporates the discrepancy between the stabilizer and the system Jacobian matrix. Provided this discrepancy is small enough, the method is shown to be A(alpha)-stable. This result is interesting for an explicit time-stepping method. Numerical experiments are presented for two classes of stiff models in cardiac electrophysiology. They include performances comparisons with several classical methods. The EAB method is observed to be as stable as implicit solvers and cheaper at equal level of accuracy.
dc.description.sponsorshipModèles numériques haute résolution de l'électrophysiologie cardiaque - ANR-13-MONU-0004
dc.description.sponsorshipL'Institut de Rythmologie et modélisation Cardiaque - ANR-10-IAHU-0004
dc.language.isoen
dc.publisherElsevier
dc.subject.enexplicit high-order multistep methods
dc.subject.enstiff equations
dc.subject.enDahlquist stability
dc.subject.enexponential integrators of Adams type
dc.subject.enstability and convergence
dc.title.enExponential Adams Bashforth integrators for stiff ODEs, application to cardiac electrophysiology
dc.typeArticle de revue
dc.identifier.doi10.1016/j.matcom.2018.04.006
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
dc.identifier.arxiv1804.09927
bordeaux.journalMathematics and Computers in Simulation
bordeaux.page15-34
bordeaux.volume153
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01394036
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01394036v1
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