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.
Corrigendum to “Existence, blow-up and exponential decay estimates for a system of nonlinear wave equations with nonlinear boundary conditions” [Math Meth Appl Sci. 37 (4) (2014) 464-487. https://doi.org/10.1002/mma.2803]