Fourth-order compact schemes with adaptive time step for monodomain reaction–diffusion equations

Multigrid applied to fourth-order compact schemes for monodomain reaction–diffusion equations in two dimensions has been developed. The scheme accounts for the anisotropy of the medium, allows for any cellular activation model to be used, and incorporates an adaptive time step algorithm. Numerical simulations show up to a 40% reduction in computational time for complex cellular models as compared to second-order schemes for the same solution error. These results point to high-order schemes as valid alternatives for the efficient solution of the cardiac electrophysiology problem when complex cellular activation models are used.