Numerical blow-up time for a semilinear parabolic equation with nonlinear boundary conditions
Summary: We obtain some conditions under which the positive solution for semidiscretizations of the semilinear equation \(u_{t}=u_{xx} - a(x,t)f(u)\), \(0<x<1\), \(t\in (0,T)\), with boundary conditions \(u_{x}(0,t)=0\), \(u_{x}(1,t)=b(t)g(u(1,t))\), 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.
scientific article; zbMATH DE number 5628315
scientific article