Journal of Applied Mathematics
Volume 2008 (2008), Article ID 753518, 29 pages
doi:10.1155/2008/753518
Research Article

Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions

Louis A. Assalé,1 Théodore K. Boni,1 and Diabate Nabongo2

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.

Abstract

We obtain some conditions under which the positive solution for semidiscretizations of the semilinear equation ut=uxx−a(x,t)f(u),  0<x<1,  t∈(0,T), with boundary conditions ux(0,t)=0, ux(1,t)=b(t)g(u(1,t)), 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.