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

In this article, 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 performance comparisons with several classical methods. The EAB method is observed to be as stable as implicit solvers and cheaper at equal level of accuracy.