Simulation of SPDEs for Excitable Media Using Finite Elements

In this paper, we address the question of the discretization of stochastic partial differential equations (SPDEs) for excitable media. Working with SPDEs driven by colored noise, we consider a numerical scheme based on finite differences in time (Euler–Maruyama) and finite elements in space. Motivated by biological considerations, we study numerically the emergence of reentrant patterns in excitable systems such as the Barkley or Mitchell–Schaeffer models.