Discretization of the Cauchy problem for a fast diffusion equation

Abstract

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 − j 2x u m = u p 1 in R, where m ∈ (0, 1), p 1 > 1, > 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.