Rush Larsen time stepping methods of high order for stiff problems in cardiac electrophysiology

Yves Coudière (1, 2, 3) , Charlie Douanla Lontsi (2, 3) , Charles Pierre (4)

1 IMB - Institut de Mathématiques de Bordeaux
2 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
3 IHU-LIRYC
4 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

The development of efficient solvers in cardiac electrophysiology requires high order (semi) explicit and stable time stepping methods. In this paper are introduced two new exponential integrators of orders 3 and 4. They generalize the order 2 Rush Larsen scheme derived by Perego and Veneziani [24] in 2009. They have been named Rush Larsen of order k, shortly RL k. The RL k schemes are explicit exponential multistep integrators. They display a simple general formulation and an easy implementation. The RL k schemes are shown to be stable under perturbation (or 0-stable) and con-vergent 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.

Mots clés: stiff equations; explicit high-order multistep methods; exponential integrators; stability and convergence; Dahlquist stability

Domaines: Analyse numérique [math.NA]

Yves Coudière, Charlie Douanla Lontsi, Charles Pierre. Rush Larsen time stepping methods of high order for stiff problems in cardiac electrophysiology. 2017. ⟨hal-01557856v1⟩