A unified analysis for reaction–diffusion models with application to the spiral waves dynamics of the Barkley model

Abstract Applying the gradient discretisation method (GDM), paper develops a comprehensive numerical analysis for nonlinear equations called reaction–diffusion model. Using only three properties, this provides convergence results several conforming and non-conforming schemes that align with GDM. As an application of analysis, hybrid mimetic mixed (HMM) model is designed, its established. Numerical experiments using HMM are presented to facilitate study creation spiral waves in Barkley ways which behave when interacting boundaries their generating medium.