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BY-NC-ND 4.0 license Open Access Published by De Gruyter January 1, 2009

An Adaptive Scheme to Handle the Phenomenon of Quenching for a Localized Semilinear Heat Equation with Neumann Boundary Conditions

  • TH. K. Kouakou EMAIL logo , TH. K. Boni and R. K. Kouakou

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.

Received: 2009-06-19
Revised: 2009-08-16
Accepted: 2009-10-26
Published Online: 2009
Published in Print: 2009

© Institute of Mathematics, NAS of Belarus

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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