Numerical blow-up for nonlinear diffusion equation with neumann boundary conditions

Abstract

This work is concerned with the study of the numerical approximation for the nonlinear diffusion equation (u)t = uxx, 0 < x < 1, t > 0, under Neumann boundary conditions ux(0, t) = 0, ux(1, t) = uα(1, t), t > 0. First, we obtain a semidiscrete scheme by the finite differences method and prove the convergence of its solution to the continuous one. Then, we establish the numerical blow-up and the convergence of the numerical blow-up time to the theoretical one when the mesh size goes to zero. Finally, we illustrate our analysis with some numerical experiments.