Abstract
This paper concerns the study of the numerical approximation for the following boundary value problem $$ \left\{ \begin{array}{ll} \hbox{$(u^{m})_{t}=u_{xx}$, $<x<1$,\; $t>0$,} \\ \hbox{$u_{x}(0,t)=0$,\quad $u_{x}(1,t)=-u^{-\beta}(1,t)$,\quad $t>0$,} \\ \hbox{$u(x,0)=u_{0}(x)>0$,\quad $0\leq x\leq 1$,} \\ \end{array} \right.$$ where $m\geq1$, $\beta>0$. We obtain some conditions under which the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time. Finally, we give some numerical experiments to illustrate our analysis.
Citation
Théodore K. Boni. Diabate Nabongo. "Numerical quenching for a nonlinear diffusion equation with a singular boundary condition." Bull. Belg. Math. Soc. Simon Stevin 16 (2) 289 - 303, May 2009. https://doi.org/10.36045/bbms/1244038140
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