Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions

We obtain some conditions under which the positive solution for semidiscretizations of the semilinear equation ut uxx − a x, t f u , 0 < x < 1, t ∈ 0, T , with boundary conditions ux 0, t 0, ux 1, t b t g u 1, t , blows up in a finite time and estimate its semidiscrete blow-up time. We also establish the convergence of the semidiscrete blow-up time and obtain some results about numerical blow-up rate and set. Finally, we get an analogous result taking a discrete form of the above problem and give some computational results to illustrate some points of our analysis.