Abstract:This paper concerns the study of the numerical approximation for the following boundary value problem: $$ \cases u_t(x,t)-u_{xx}(x,t) = -u^{-p}(x,t), & 0<x<1, t>0, u_{x}(0,t)=0, & u(1,t)=1, t>0, u(x,0)=u_{0}(x)>0, & 0\leq x \leq 1, \endcases $$ where $p>0$. 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.
Keywords: semidiscretizations, discretizations, heat equations, quenching, semidiscrete quenching time, convergence
AMS Subject Classification: 35K55, 35B40, 65M06