Quenching for semidiscretizations of a semilinear heat equation with Dirichlet and Neumann boundary conditions

This paper concerns the study of the numerical approximation for the following boundary value problem: 8><>: ut(x, t) − uxx(x, t) = −u(x, t), 0 < x < 1, t > 0, ux(0, t) = 0, u(1, t) = 1, t > 0, u(x, 0) = u0(x) > 0, 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. Finally, we give some numerical experiments to illustrate our analysis.