Numerical simultaneous blow-up of the solution of a parabolic system with three components

Abstract

In this paper, we study a numerical approximation of a parabolic system with three components. Under some assumptions, we prove that the solution of a semidiscrete form of above problem blows up at the center point in a finite time and estimate its semidiscrete blow-up time. We show that the semidiscrete simultaneous blow-up occurs. We also establish the convergence of the semidiscrete simultaneous blow-up time to the theoretical one when the mesh size tends to zero. Finally, we give some numerical experiments to illustrate our analysis.