Discretization of the Cauchy problem for a fast diffusion equation

摘要

In this paper, we propose and study a fully discretization for computing the positive and (possibly) blowing-up solution of the Cauchy problem: ut-∂x2um=αup1 in R, where m∈(0,1), p1>1, α>0, with an initial condition u0 assumed to be a nonnegative and continuous function with compact support. The convergence of the numerical method is proved.