  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.
