Splitting schemes for FitzHugh–Nagumo stochastic partial differential equations

Journal article, 2023

We design and study splitting integrators for the temporal discretization of the stochastic FitzHugh–Nagumo system. This system is a model for signal propagation in nerve cells where the voltage variable is the solution of a one-dimensional parabolic PDE with a cubic nonlinearity driven by additive space-time white noise. We first show that the numerical solutions have finite moments. We then prove that the splitting schemes have, at least, the strong rate of convergence 1/4. Finally, numerical experiments illustrating the performance of the splitting schemes are provided.