Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions

Abstract

We obtain some conditions under which the positive solution for semidiscretizations of the semilinear equationut=uxx−a(x,t)f(u),  0<x<1,  t∈(0,T), with boundary conditionsux(0,t)=0,ux(1,t)=b(t)g(u(1,t)), blows up in a finite time and estimate its semidiscrete blow-up time. We also establish the convergence of the semidiscrete blow-up time and obtain some results about numerical blow-up rate and set. Finally, we get an analogous result taking a discrete form of the above problem and give some computational results to illustrate some points of our analysis.