SIMULTANEOUS NUMERICAL BLOW-UP IN A FOUR-COMPONENT SYSTEM OF HEAT EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

This paper investigates the numerical approximation of a system of heat equations with nonlinear boundary conditions. We prove that the solution of a semidiscrete form of above problem blows up in a finite time. We also establish certain conditions under which simultaneous blow-up occurs for the solution of the semidiscrete problem. After showing that the numerical blow-up time converges to the theoretical blow-up time as the mesh size tends to zero, we finally present some numerical results to illustrate key points of our work.