Charlie Douanla Lontsi ; Yves Coudière ; Charles Pierre - Efficient high order schemes for stiff ODEs in cardiac electrophysiology

arima:2668 - Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, April 25, 2018, Volume 28 - 2018 - 2019 - Mathematics for Biology and the Environment -
Efficient high order schemes for stiff ODEs in cardiac electrophysiologyArticle

Authors: Charlie Douanla Lontsi 1,2; Yves Coudière ORCID3,4,2; Charles Pierre 5

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.

Volume: Volume 28 - 2018 - 2019 - Mathematics for Biology and the Environment
Published on: April 25, 2018
Accepted on: April 14, 2018
Submitted on: January 26, 2017
Keywords: Exponential schemes, stiff ordinary differential equations, high order schemes, cardiac electrophysiology,high order schemes,cardiac electrophysiology,stiff ordinary differential equations, [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA]
    Source : HAL
  • Modèles numériques haute résolution de l'électrophysiologie cardiaque; Funder: French National Research Agency (ANR); Code: ANR-13-MONU-0004

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