High-Order Operator Splitting for the Bidomain and Monodomain Models

Abstract

The bidomain and monodomain models are multiscale reaction-diffusion models that describe the electrical activity in myocardial tissue. Because of the size and specific structure of the system required to produce meaningful data, numerical solutions are often found through the application of operator-splitting (OS) methods. First- and second-order OS methods have been successfully implemented for finding numerical solutions of the bidomain and monodomain models. It is well known that OS methods with order higher than two require backward time integration within each step. Accordingly, one may conclude that splitting methods with order higher than two are not suitable for models that contain deterministic parabolic equations because the necessary backward time integration would cause instabilities. In this paper, we demonstrate that it is indeed possible to obtain stable results from third-order OS methods applied to the bidomain and monodomain models. Furthermore, we demonstrate that the accompanying gain...