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Ganon Ardjouma,N'Dri Kouakou Cyrille,Edja Kouame Beranger,Toure Kidjegbo Augustin 원광대학교 기초자연과학연구소 2023 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.26 No.3
This work is concerned with the study of the numerical approximation for the nonlinear diffusion equation $(u^{m})_t=u_{xx}$, $0<x<1, t>0$, with a singular boundary outfluxes $u_x(0,t)=u^{-p}(0,t)$, $u_x(1,t)=-u^{-q}(1,t)$, $t>0$. We use the finite differences method to obtain a semidiscrete scheme of the above problem. First, we give appropriate conditions under which the semidiscrete solution quenches in a finite time and estimate its semidiscrete quenching time. Then, we establish the convergence of the semidiscrete quenching time. Finally, we illustrate our analysis with some numerical experiments.