Journal of Applied Mathematics
Volume 2008 (2008), Article ID 753518, 29 pages
Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions
1Institut National Polytechnique Houphouët-Boigny de Yamoussoukro, BP 1093, Yamoussoukro, Cote D'Ivoire
2Département de Mathématiques et Informatiques, Université d'Abobo-Adjamé, UFR-SFA, 16 BP 372 Abidjan 16, Cote D'Ivoire
Received 29 April 2008; Revised 15 December 2008; Accepted 29 December 2008
Academic Editor: Jacek Rokicki
Copyright © 2008 Louis A. Assalé et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We obtain some conditions under which the positive solution for
semidiscretizations of the semilinear equation , with boundary conditions , , blows up in a finite time and estimate its semidiscrete blow-up time. We also establish
the convergence of the semidiscrete blow-up time and obtain some results about
numerical blow-up rate and set. Finally, we get an analogous result taking
a discrete form of the above problem and give some computational results to
illustrate some points of our analysis.