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Mathematics > Numerical Analysis

arXiv:2407.07834 (math)
[Submitted on 10 Jul 2024]

Title:Generic Numerical Analysis of Stochastic Reaction Diffusion Model with applications in excitable media

Authors:Yahya Alnashri, Hasan Alzubaidi
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Abstract:The stochastic reaction-diffusion model driven by a multiplicative noise is examined. We construct the gradient discretisation method (GDM), an abstract framework combining several numerical method families. The paper provides the discretisation and proves the convergence of the approximate schemes using a compactness argument that works under natural assumptions on data. We also investigate, using a finite volume method, known as the hybrid mixed mimetic (HMM) approach, the effects of multiplicative noise on the dynamics of the travelling waves in the excitable media displayed by the model. Particularly, we consider how sufficiently high noise can cause waves to backfire or fail to propagate.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2407.07834 [math.NA]
  (or arXiv:2407.07834v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2407.07834

Submission history

From: Yahya Alnashri [view email]
[v1] Wed, 10 Jul 2024 16:54:48 UTC (1,369 KB)
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