一类多维非线性反应扩散方程有限差分格式的稳定性问题(英文)  

STABILITY PROBLEM OF THE FINITE DIFFERENCE SCHEME FOR A MULTIDIMENSIONAL NONLINEAR REACTION-DIFFUSION EQUATION

作　　者：徐琛梅[1] 王波[1] 王秀琴[1] 

机构地区：[1]河南大学数学与信息科学学院,河南开封475001

出　　处：《数学杂志》2012年第3期415-422,共8页Journal of Mathematics

基　　金：Supported by the Natural Science Foundation of the Education Department of Henan Province(2010A100003);National Natural Science Foundation of China(40805020)

摘　　要：本文研究了一类多维线性反应扩散方程差分格式的稳定性.利用量未知元方法,建立了具有增量未知元的有限差分格式;然后利用非线性Galerkin方法,得到该差分格式的稳定性条件.通过对该格式的稳定性分析,说明和经典的差分格式的稳定性相比较,带有增量未知元的有限差分格式的稳定性得到了提高.In this paper,stability of the difference scheme for a multidimensional nonlinear reaction-diffusion equation is studied.Using incremental unknowns method,the finite difference scheme with incremental unknowns is established.Then the stability condition of the scheme is obtained by means of nonlinear Galerkin method.Through stability analysis for the scheme,it is shown that stability of the finite difference scheme with the incremental unknowns is improved when compared with that of the corresponding classical difference scheme.

关 键 词：有限差分 反应扩散方程 增量未知元 稳定性分析 

分 类 号：O241.84[理学—计算数学]