Blow-Up for Discretization of a Localized Semilinear Heat Equation
Théodore K. Boni, Halima Nachid, Diabaté Nabongo · Annals of the Alexandru Ioan Cuza University - Mathematics · 2010
This paper concerns the study of the numerical approximation for the following initial-boundary value problem:and γ is a positive parameter.Under some assumptions, we prove that the solution of a discrete form of the above problem blows up in a finite time and estimate its numerical blow-up time.We also show that the numerical blow-up time in certain cases converges to the real one when the mesh size tends to zero.Finally, we give some numerical experiments to illustrate our analysis.