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Mathematics > Numerical Analysis

arXiv:2207.10484 (math)
[Submitted on 21 Jul 2022]

Title:Splitting schemes for FitzHugh--Nagumo stochastic partial differential equations

Authors: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.
Subjects: Numerical Analysis (math.NA); Probability (math.PR)
Cite as: arXiv:2207.10484 [math.NA]
  (or arXiv:2207.10484v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2207.10484

Submission history

From: Charles-Edouard Bréhier [view email]
[v1] Thu, 21 Jul 2022 13:59:51 UTC (7,818 KB)
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