A non‐linear model of cerebral diffusion: stability of finite differences method and resolution using the Adomian method

This paper describes a non‐linear reaction‐diffusion equation, which models how a substance spreads in the surface of the cortex so as to avoid a massive destruction of neurones when cerebral tissue is not oxygenated correctly. For the explicit finite differences method, the necessary stability condition is provided by a reaction‐diffusion equation with non‐linearity given by a decreasing function. The solution to the non‐linear reaction‐diffusion equation of the model can be obtained via one of the two methods: the finite differences (explicit schema) method and the Adomian method.