HOC simulation of Barkley model in excitable media

Excitable media have been extensively used to study the pattern formations, most prominently the spiral wave (2D) and the scroll wave (3D) patterns in chemical reaction, cardiac tissue, etc. through different forms of the Barkley model, governed by a system of nonlinear reaction-diffusion (R-D) equations. To the best of our knowledge, most of the previous numerical results have been obtained by explicit schemes which are conditionally stable and lower order accurate. In the current study, we reconstruct an existing higher order compact (HOC) finite difference scheme to discretize the highly nonlinear equations governing the patterns. The scheme which is implicit in nature and unconditionally stable is seen to efficiently capture the patterns. Furthermore, we also determine the spiral tip path by post processing our HOC data where we specifically deal with petal formations arising out of the tip trajectories.