NUMERICAL QUENCHING FOR A SEMILINEAR PARABOLIC EQUATION

This paper concerns the study of the numerical approximation for the nonlinear parabolic boundary value problem with the source terra leading to the quenching ill finite time. We find some conditions under which the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its semidiscrete quenching tinge. We also prove that the semidiscrete quenching time converges to the real one when the mesh size goes to zero. A similar study has been also investigated taking a discrete form of the above problem. Finally, we give some numerical experiments to illustrate our analysis.