On the Computation of the Numerical Blow-Up Time for Solutions of Semilinear Parabolic Equation

Blow-up for Semidiscretization of Semilinear Parabolic Equation With Nonlinear Boundary Condition

“…Since the solution u blows up in finite time, it is worth asking what can be stated about numerical approximations of this type of problems. For previous work on numerical approximations of blowing up solutions we refer to (Abia, López-Marcos, & Martínez, 1996;Adou, Touré, & Coulibaly, 2019;Assalé et al, 2008;Dratman, 2010;Edja, Touré, & Koua, 2018;Ganon, Taha, & Touré, 2019;N'dri, Touré, & Yoro, 2018;Touré, N'Guessan, & Diabate, 2015;Taha, Touré, & Mensah, 2012 and references therein). This paper is structured as follows : in section 2, we introduce a semidiscrete scheme of the problem (1).…”

“…• The numerical method used in this paper has some advantages. Firstly, to obtain the numerical blow-up, we are not obliged to put an additional condition on the initial data, which is not the case of some numerical methods (see Theorem 4.3, Theorem 8.6 in (Assalé et al, 2008) and Theorem 6 in (Adou et al, 2019)). Secondly, when the mesh size goes to zero, that is I becomes large, with the method of this paper, the number of iterations n increases slowly.…”