In this paper, we obtain under some conditions, convergence of the blow-up time T for semidiscretization of semilinear heat  equation in  with boundary conditions   and initial condition   Then we estimate the numerical blow-up time by applying an efficient numerical algorithm to the semidiscrete problem. Finally, some results are presented to illustrate our analysis.

blow-up time, Aitken Δ² method, semidiscretization, finite differences, arc length transformation.