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Article Dans Une Revue Electronic Transactions on Numerical Analysis Année : 2020

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

Résumé

To address the issues of stability and accuracy for reaction-diffusion equations, the development of high order and stable time-stepping methods is necessary. This is particularly true in the context of cardiac electrophysiology, where reaction-diffusion equations are coupled with stiff ODE systems. Many research have been led in that way in the past 15 years concerning implicit-explicit methods and exponential integrators. In 2009, Perego and Veneziani proposed an innovative time-stepping method of order 2. In this paper we present the extension of this method to the orders 3 and 4 and introduce the Rush-Larsen schemes of order k (shortly denoted RL_k). The RL_k schemes are explicit multistep exponential integrators. They display a simple general formulation and an easy implementation. The RL_k schemes are shown to be stable under perturbation and convergent 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. The RL k schemes are shown to be stable under perturbation and convergent oforder 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.
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Dates et versions

hal-01557856 , version 1 (06-07-2017)
hal-01557856 , version 2 (27-11-2017)
hal-01557856 , version 3 (11-06-2019)

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Citer

Yves Coudière, Charlie Douanla Lontsi, Charles Pierre. Rush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology. Electronic Transactions on Numerical Analysis, 2020, 55, pp.342-357. ⟨hal-01557856v3⟩
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