DOI: 10.2478/s11533-007-0031-3 Research article CEJM 5(4) 2007 751–763 A Numerical Approach of the sentinel method for distributed parameter systems Aboubakari Traore 1∗ , Benjamin Mampassi 2† , Bisso Saley 3‡ 1 Dept. of Mathematics and Computer Science, Cheikh Anta Diop University, Dakar, Senegal 2 Dept. of Mathematics Computer Science, Cheikh Anta Diop University, Dakar, Senegal 3 Dept. of Mathematics, Niamey University, Niamey, Niger. Received 03 May 2007; accepted 28 August 2007 Abstract: In this paper we consider the problem of detecting pollution in some non linear parabolic systems using the sentinel method. For this purpose we develop and analyze a new approach to the discretization which pays careful attention to the stability of the solution. To illustrate convergence properties we give some numerical results that present good properties and show new ways for building discrete sentinels. c  Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved. Keywords: Sentinel method, collocation method, Chebyshev differentiation matrix, Gauss–Legendre points and weight matrix MSC (2000): 65M70; 65N22 1 Introduction Let us consider the following boundary value problem: ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ ∂y ∂t (t, x) - ∂ 2 y ∂x 2 (t, x)+ F (y (t, x)) = ξ (t, x)+ λ  ξ (t, x) in Q y (t, x) = 0 on ∑ y (0,x) = y 0 (x)+ τ  y 0 (x) on Ω (1) where • Q =]0,T [×Ω, with Ω =] - 1, 1[ , T> 0, and ∑ = (0,T ) × ∂ Ω, • F : R -→ R is a locally lipschitzian function satisfying the following: there exists ∗ E-mail: traboubakari@yahoo.fr † E-mail: mampassi@hotmail.com ‡ E-mail: bsaley@yahoo.fr