An adaptive method on the quenching time of a nonlinear parabolic equation with respect to the non-linear source and neumann conditions

In this paper, we introduce a new adaptive method for computing the numerical solutions of a class of quenching parabolic equations which exhibit a solution with one singularity. The continuity of the quenching time is studied in this paper where we have considered a parabolic equation with variable reaction which quenches in a finite time. For this fact, we have estimated the quenching time and have proved that it is continuous as a function of the nonlinear source for the following boundary value problem...