The Euler method in the numerical integration of reaction–diffusion problems with blow-up Original Research Article

A fully discretized scheme, where the Euler method is used for the numerical integration in time, is considered for the approximation of the solutions with blow-up of reaction–diffusion problems. The convergence of the blow-up times of the numerical solutions to the theoretical one is proved, when the time steps are suitable chosen, in three situations: blow-up of the first Fourier coefficient, symmetric solutions and reaction functions with f(0)=0. Hence, our analysis shows the key role played by the time-stepping strategies.