Efficient high order schemes for stiff ODEs in cardiac electrophysiology
For researchers in cardiac electrophysiology, this work demonstrates that explicit high-order exponential solvers can efficiently handle stiff ODEs, enabling accurate large-time-step computations.
The paper analyzes high-order exponential solvers for stiff ODEs in cardiac electrophysiology, showing that these explicit methods allow large time steps comparable to implicit methods while achieving significant cost savings for a given accuracy.
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.