NUMERICAL QUENCHING FOR A NONLINEAR DIFFUSION EQUATION WITH SINGULAR BOUNDARY FLUX

In this paper, we study the semidiscrete approximation of the solution of a nonlinear diffusion equation with nonlinear source and singular boundary flux. We find some conditions under which the solution of the semidiscrete form quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time to the theoretical one when the mesh size tends to zero. Finally, we give some numerical experiments for a best illustration of our analysis.