Blow-up for Semidiscretization of Semilinear Parabolic Equation With Nonlinear Boundary Condition

This paper deals with the study of the numerical approximation for the following semilinear equation with a nonlinear absorption term ut = uxx− λup, 0 < x < 1, t > 0, and a nonlinear flux boundary condition ux(0,t) = 0, ux(1,t) = uq(1,t), t > 0. We give conditions under which the positive semidiscrete solution blows up in a finite time. Convergence of the numerical blow-up time to the theoretical one when the mesh size goes to zero is established. Finally, we use an efficient algorithm to estimate the blow-up time.