Affiliations: Université d'Abobo-Adjamé, UFR-SFA, Département de Mathématiques et Informatiques, 16 BP 372 Abidjan 16, Côte d'Ivoire. E-mail: [email protected] | Institut National Polytechnique Houphouët-Boigny de Yamoussoukro, BP 1093 Yamoussoukro, Côte d'Ivoire. E-mail: [email protected]
Abstract: We obtain some conditions under which the positive solution of the numerical approximation for the heat equation ut(x, t)=uxx(x, t), x∈(0, 1), t>0, with the singular boundary condition ux(1, t)=−u−β(1, t), where β>0 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 and set. Finally we give some numerical results to illustrate our analysis.
Keywords: semidiscretizations, singular boundary condition, quenching, semidiscrete quenching time, convergence, numerical quenching rate, numerical quenching set
