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.

翻译：本文研究了由乘性噪声驱动的随机反应扩散模型。我们构建了梯度离散化方法（GDM），这是一种融合了多种数值方法族的抽象框架。论文给出了离散化方案，并利用紧致性论证证明了近似格式在数据满足自然假设条件下的收敛性。此外，我们采用一种称为混合混合模仿（HMM）方法的有限体积法，探究了乘性噪声对模型所展示的可激发介质中行波动力学的影响。特别地，我们考察了足够强的噪声如何导致波反向传播或传播失败。