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                <term xml:lang="en">Exponential schemes</term>
                <term xml:lang="en"> high order schemes</term>
                <term xml:lang="en"> cardiac electrophysiology</term>
                <term xml:lang="en"> stiff ordinary differential equations</term>
                <term xml:lang="fr">Electrophysiologie cardiaque</term>
                <term xml:lang="fr">schémas d’ordre élevé</term>
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              <p>In this work we analyze the resort to high order exponential solvers for stiff ODEs in the context of cardiac electrophysiology modeling. The exponential Adams-Bashforth and the Rush-Larsen schemes will be considered up to order 4. These methods are explicit multistep schemes.The accuracy and the cost of these methods are numerically analyzed in this paper and benchmarked with  several classical explicit and implicit schemes at various orders. This analysis has been led considering data of high particular interest in cardiac electrophysiology : the activation time ($t_a$ ), the recovery time ($t_r $) and the action potential duration ($APD$). The Beeler Reuter ionic model, especially designed for cardiac ventricular cells, has been used for this study. It is shown that, in spite of  the stiffness of the considered model, exponential solvers allow computation at large time steps, as large as for implicit methods. Moreover, in terms of cost for a given accuracy, a significant gain is achieved with exponential solvers. We conclude that accurate computations at large time step are possible with explicit high order methods. This is a quite important feature when considering stiff non linear ODEs.</p>
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              <p>Dans ce travail, nous analysons le recours aux solveurs exponentiels d’ordre élevé pourdes EDO raides dans le contexte de la modélisation en électrophysiologie cardiaque. Nous nousintéressons en particulier aux schémas exponentiels Adams Bashforth et Rush Larsen de l’ordre 2à 4. Ces schémas sont explicites et multi-pas. La précision et le coût de ces méthodes sont analysésnumériquement et comparés avec plusieurs schémas explicites et implicites classiques à diversordres. Cette analyse nous permet de calculer des valeurs informatives qui ont un interêt particulieren électrophysiologie cardiaque: Le temps d’activation (ta), le temps de restitution (tr) et la durée dupotentiel d’action (APD). L’étude est faite à travers le modèle ionique Beeler Reuter, spécialementconçu pour les cellules ventriculaires cardiaques. Nous montrons que malgré la raideur des équations,les schémas exponentiels permettent de faire des calculs à des pas de temps aussi grand quepour des schémas implicites. De plus pour une précision donnée, un gain significatif en terme de coûtest obtenu avec des solveurs exponentiels. Nous concluons qu’il est possible de faire des calculsprécis à des grands échelles de temps avec des schémas explicites d’ordre élevé. Ce qui est unecaractéristique très importante quand il s’agit des EDO raides et non linéaires.</p>
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          <desc>Modèles numériques haute résolution de l'électrophysiologie cardiaque</desc>
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