On the blow-up time convergence of semidiscretizations of reaction-diffusion equations Original Research Article

Semidiscretizations of reaction-diffusion equations are studied and special attention is devoted to symmetric solutions. Also nonsymmetric solutions are considered when the reaction term is such that f(0) = 0. Sufficient conditions for blow-up in such discretizations are established and upper bounds of the blow-up time, which depend on the maximum norm of the initial conditions, are provided. Convergence of the blow-up times of the semidiscrete problems to the theoretical one is proved.