Rush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology
| hal.structure.identifier | IHU-LIRYC | |
| hal.structure.identifier | Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | COUDIÈRE, Yves | |
| hal.structure.identifier | IHU-LIRYC | |
| hal.structure.identifier | Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DOUANLA LONTSI, Charlie | |
| hal.structure.identifier | Laboratoire de Mathématiques et de leurs Applications [Pau] [LMAP] | |
| dc.contributor.author | PIERRE, Charles | |
| dc.date.accessioned | 2024-04-04T03:01:04Z | |
| dc.date.available | 2024-04-04T03:01:04Z | |
| dc.date.created | 2018-10-15 | |
| dc.date.issued | 2020-07-14 | |
| dc.identifier.issn | 1068-9613 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192869 | |
| dc.description.abstractEn | To 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.sponsorship | Modèles numériques haute résolution de l'électrophysiologie cardiaque - ANR-13-MONU-0004 | |
| dc.language.iso | en | |
| dc.publisher | Kent State University Library | |
| dc.subject.en | explicit high-order multistep methods | |
| dc.subject.en | stiff equations | |
| dc.subject.en | stability and convergence | |
| dc.subject.en | exponential integrators | |
| dc.subject.en | Dahlquist stability | |
| dc.title.en | Rush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| dc.identifier.arxiv | 1712.02260 | |
| bordeaux.journal | Electronic Transactions on Numerical Analysis | |
| bordeaux.page | 342-357 | |
| bordeaux.volume | 55 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01557856 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01557856v1 | |
| bordeaux.COinS | ctx_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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