Numerical solution of a nonlinear reaction diffusion equation

被引：4
|
作者：
Le Roux, AY [1 ]
Le Roux, MN [1 ]
机构：
[1] Univ Bordeaux 1, UMR 5467, LaBAG, F-33405 Talence, France
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2005年 / 173卷 / 02期
关键词：
nonlinear reaction diffusion equation; finite-time blowup;
D O I：
10.1016/j.cam.2004.03.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the authors propose a numerical method to compute the solution of a Cauchy problem with blow-up of the solution. The problem is split in two parts: a hyperbolic problem which is solved by using Hopf and Lax formula and a parabolic problem solved by a backward linearized Euler method in time and a finite element method in space. It is proved that the numerical solution blows up in a finite time as the exact solution and the support of the approximation of a self-similar solution remains bounded. The convergence of the scheme is obtained. (C) 2004 Elsevier B.V. All rights reserved.
引用
收藏
页码：211 / 237
页数：27
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