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

This work is concerned with the study of the numerical approximation for the nonlinear diffusion equation (u m ) t = u xx , 0 < x < 1, t > 0, under Neumann boundary conditions u x (0, t) = 0, u x (1, t) = u α (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. [ABSTRACT FROM AUTHOR]

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