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Models in cardiac electrophysiology are coupled systems of reaction diffusionPDE and of ODE. The ODE system displays a very stiff behavior. It is non linearand its upgrade at each time step is a preponderant load in the computationalcost. The issue is to develop high order explicit and stable methods to copewith this situation.In this article, is is analyzed the resort to exponentialAdams Bashforth (EAB) integrators in cardiac electrophysiology. The method ispresented in the framework of a general and varying stabilizer, that is wellsuited in this context. Stability under perturbation (or 0-stability) isproven. It provides a new approach for the convergence analysis of the method.The Dahlquist stability properties of the method is performed. It is presentedin a new framework that incorporates the discrepancy between the stabilizer andthe system Jacobian matrix. Provided this discrepancy is small enough, themethod is shown to be A(alpha)-stable. This result is interesting for anexplicit time-stepping method. Numerical experiments are presented for twoclasses of stiff models in cardiac electrophysiology. They include performancescomparisons with several classical methods. The EAB method is observed to be asstable as implicit solvers and cheaper at equal level of accuracy.

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