Numerical quenching of a heat equation with nonlinear boundary conditions

Volume 13, Issue 1, pp 65--74 http://dx.doi.org/10.22436/jnsa.013.01.06
Publication Date: September 11, 2019 Submission Date: April 10, 2019 Revision Date: June 15, 2019 Accteptance Date: June 16, 2019

Authors

Kouame Beranger Edja - Institut National Polytechnique Felix Houphouet-Boigny Yamoussoukro, BP 2444, Cote d'Ivoire. Kidjegbo Augustin Toure - Institut National Polytechnique Felix Houphouet-Boigny Yamoussoukro, BP 2444, Cote d'Ivoire. Brou Jean-Claude Koua - UFR Mathematique et Informatique, Universite Felix Houphouet Boigny, Cote d'Ivoire.


Abstract

In this paper, we study the quenching behavior of semidiscretizations of the heat equation with nonlinear boundary conditions. We obtain some conditions under which the positive solution of the semidiscrete problem quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time and obtain some results on numerical quenching rate. Finally we give some numerical results to illustrate our analysis.


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