Numerical Quenching solutions of Localized Semilinear Parabolic Equation with a Variable Reaction

In this paper, we study the semidiscrete approximation for the following initial-boundary value problem where p( x )C l , symmetric and non decreasing on the interval (-l,0), inf x(-l,0) p(x) .1 and 2 1 . We prove, under suitable conditions on p(x) and initial datum, that the semidiscrete solution quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time to the theoretical one when the mesh size tends to zero. Finally, we give some numerical experiments for a best illustration of our analysis