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arXiv · 2207.10484

Splitting schemes for FitzHugh--Nagumo stochastic partial differential equations

Charles-Edouard Bréhier·David Cohen·Giuseppe Giordano
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Abstract

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.

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Charles-Edouard Bréhier, David Cohen, Giuseppe Giordano. 2022-07-21. Splitting schemes for FitzHugh--Nagumo stochastic partial differential equations. https://arxiv.org/abs/2207.10484

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