Numerical solution of fast diffusion or slow diffusion equations

In this paper, the author proposes a semi-discretization in time of a nonlinear reaction diffusion equation (fast or slow diffusion), the solution of which may vanish or blow up in a finite time. The approximate value at each time step is solution of a nonlinear equation which is solved by using an iterative method. It is proved that if the exact solution vanishes or blows up in a finite time, it is the same for the numerical solution.