Volume 30, pp. 247-257, 2008.

Numerical blow-up solutions for some semilinear heat equations

Firmin K. N'Gohisse and Théodore K. Boni

Abstract

This paper concerns the study of the numerical approximation for the following initial-boundary value problem, ut=uxx+bxux+up,x(0,1),t(0,T),ux(0,t)=0,u(1,t)=0,t(0,T),u(x,0)=u0(x),x[0,1], where b>0 and p>1. We give some conditions under which the solution of a semidiscrete form of the above problem blows up in a finite time and estimate its semidiscrete blow-up time. Under some assumptions, we also show that the semidiscrete blow-up time converges to the continuous blow-up time when the mesh size goes to zero. Finally, we give some numerical results to illustrate our analysis.

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Key words

semidiscretizations, discretizations, semilinear heat equations, semidiscrete blow-up time

AMS subject classifications

35B40, 35K65, 65M06