Abstract:
The numerical simulation of the bidomain equations for cardiac tissue is complicated by the fact that the inversion of a large matrix is required at every time step. Thus, the search for efficient and accurate numerical methods is not restricted to fully explicit methods. Indeed, we find that among the explicit, semi-implicit and Crank-Nicolson methods for time-stepping, when coupled with multigrid matrix inversion, the Crank-Nicolson is both the most efficient and accurate numerical method, allowing large time steps without loss of stability and less loss of accuracy than competing methods. Thus, the Crank-Nicolson method is the preferred ``first try'' for numerical integration of the bidomain equations.