Discretization of the Cauchy problem for a fast diffusion equation

In this paper, we propose and study a fully discretization for computing the positive and (possibly) blowing-up solution of the Cauchy problem: u t - ∂ x 2 u m = α u p 1 in R , where m ∈ ( 0 , 1 ) , p 1 > 1 , α > 0 , with an initial condition u 0 assumed to be a nonnegative and continuous function with compact support. The convergence of the numerical method is proved.