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We obtain some conditions under which the positive solution forsemidiscretizations 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 establishthe convergence of the semidiscrete blow-up time and obtain some results aboutnumerical blow-up rate and set. Finally, we get an analogous result takinga discrete form of the above problem and give some computational results toillustrate some points of our analysis

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