Numerical quenching solutions of localized semilinear parabolic equation

This paper concerns the study of the numerical approximationfor the following initial-boundary value problem:ut(x; t) = uxx(x; t) + E(1 - u(0; t))-p; (x; t) 2 (-l; l) x (0; T),u(-l; t) = 0; u(l; t) = 0; t in (0; T),u(x; 0) = u0(x) and gt;= 0; x in (-l; l),where p and gt; 1, l = 1/2 and E and gt; 0....