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 u(t) = u(xx) - a(x, t)f(u), 0 < x < 1, t is an element of (0, T), with boundary conditions u(x)(0, t) = 0, u(x)(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. Copyright (C) 2008 Louis A. Assale et al.