An efficient high-order compact approach for spiral wave dynamics by the FHN model

Abstract

We simulate spiral waves through the famous Fitzhugh–Nagumo (FHN) model of excitable media by employing zero flux and periodic boundary conditions. This model has been solved numerically by modifying a recently developed implicit high-order compact (HOC) finite difference scheme. We also propose a novel approach for implementing the HOC scheme on boundaries of the domain for the periodic boundary conditions. Henceforth, we investigate the effects of the zero flux and periodic boundary conditions on the patterns in excitable media and the resulting dynamics. The introduction of periodic boundary conditions is seen to trigger the breakup of the spiral waves as opposed to the ones found by imposing no-flux boundary conditions. Our computed grid independent solutions are found to be extremely close to well-known numerical results. In the process, we also probe the unconditional stability of the HOC discretization for the FHN model.