Spirals in excitable media: the free-boundary limit with diffusion

We solve numerically for the steady-state spiral in the thin-interface limit, including the effects of diffusion of the slow field. The calculation is performed using a generalization of the hybrid scheme of Keener. In this method, the diffusion equation is solved on a suitable mapped lattice while the eikonal equation relating the field on the interface to the interfacial velocity and curvature is solved independently. We present results for the selected frequency and tip radius as a function of the various parameters. We note that a stability analysis based on these results may be performed.