NUMERICAL QUENCHING FOR A SEMILINEAR PARABOLIC EQUATION

This paper concerns the study of the numerical approximation for the following boundary value problem: { u(t)(x, t) - u(xx)(x, t) = -u(-p)(x, t), 0 < x < 1, t > 0, u(0, t) = 1, u(1, t) = 1, t > 0, u(x, 0) = u0(x), 0 <= x <= 1, where p > 0. We obtain some conditions under which the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time and construct two discrete forms of the above problem which allow us to obtain some lower bounds of the numerical quenching time. Finally, we give some numerical experiments to illustrate our theoretical analysis.