TITLE

AN ADAPTIVE SCHEME TO HANDLE THE PHENOMENON OF QUENCHING FOR A LOCALIZED SEMILINEAR HEAT EQUATION WITH NEUMANN BOUNDARY CONDITIONS

AUTHOR(S)
Kouakou, Th. K.; Boni, Th. K.; Kouakou, R. K.
PUB. DATE
October 2009
SOURCE
Computational Methods in Applied Mathematics;2009, Vol. 9 Issue 4, p339
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
This paper concerns the study of the numerical approximation for the following initial-boundary value problem: { ut(x, t) = uxx(x, t) - f(u(1/2, t)), (x, t) ϵ (0,1) x (0, T), ux(0,t) = 0, ux(1,t) = 0, t ϵ (0,T), I u(x,0)=uo(x), x ϵ[0,1], where f: (0, ∞) → (0, ∞) is a C1 convex, nonincreasing function, ∫0αy dσ/f(σ) <∞ for any positive real a, lim s→0+ f(s) = ∞. The initial datum u0 ϵ C0([0, 1]), u0(x) > 0, x ϵ [0, 1]. S Under some assumptions, we prove that the solution of a discrete form of the above problem quenches in a finite time and estimate its numerical quenching time. We also show that the numerical quenching time in certain cases converges to the real one when the mesh size tends to zero. Finally, we give some numerical experiments to illustrate our analysis.
ACCESSION #
47878289

 

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