Splitting schemes for FitzHugh–Nagumo stochastic partial differential equations

07/21/2022

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by   Charles-Edouard Bréhier, et al.

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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 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.