An Adaptive Scheme to Handle the Phenomenon of Quenching for a Localized Semilinear Heat Equation with Neumann Boundary Conditions
TH. K. Kouakou, Théodore K. Boni, R. K. Kouakou · Computational Methods in Applied Mathematics · 2009
Abstract Under some assumptions, we prove that the solution of a discrete form of the above problem quenches in a finite time and estimate its numerical quenching time. We also show that the numerical quenching 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.