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A Numerical Approach of the sentinel method for distributed parameter systems

Aboubakari Traore;  Benjamin Mampassi;  Bisso Saley — 2007

Open Mathematics

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.

Full discretization of some reaction diffusion equation with blow up

Geneviève Barro;  Benjamin Mampassi;  Longin Some;  Jean Ntaganda;  Ousséni So — 2006

Open Mathematics

This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow - up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.

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