On the blow-up of finite difference solutions to the heat-diffusion equation with semilinear dynamical boundary conditions

In this paper we analyse three known finite difference schemes applied to the heat-diffusion equation with semilinear dynamical boundary conditions. We prove that the numerical blow-up times converge to the continuous ones. Also, the number of peaks of the solutions is studied. Numerical experiments are discussed and at the same time, certain interesting properties of the continuous solutions are predicted.