2024/07/10 by Yahya Alnashri, Alnashri, Yahya, Alzubaidi, Hasan
Computer Science · Physics and Astronomy · #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Numerical Analysis (math.NA) #Quantum chaos and dynamical systems #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2407.07834
openalex publication_date 2024/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.