Numerical Solution of a parabolic system with blowup of the solution

Marie-Noëlle Le Roux (1)

1 IMB - Institut de Mathématiques de Bordeaux

In this paper, the author proposes a numerical method to solve a parabolic system of two quasilinear equations of nonlinear heat conduction with sources. The solution of this system may blow up in finite time. It is proved that the numerical solution also may blow up in finite time and an estimate of this time is obtained. The convergence of the scheme is obtained for particular values of the parameters.

Mots clés: nonlinear reaction diffusion system; finite time blowup

Domaines: Analyse numérique [math.NA]

Marie-Noëlle Le Roux. Numerical Solution of a parabolic system with blowup of the solution. 2009. ⟨hal-00385043⟩