一类高维非线性反应扩散方程有限差分格式的稳定性  

Stability of the Finite Difference Scheme for a Higher Dimensional Nonlinear Reaction-Diffusion Equation

作　　者：徐琛梅[1] 于吉亮[1] 王波[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：《中山大学学报（自然科学版）》2011年第6期12-15,共4页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：河南省教育厅自然科学研究计划资助项目(2010A100003);国家自然科学青年基金资助项目(40805020)

摘　　要：利用增量未知元方法,对一类高维非线性反应扩散方程,建立具有增量未知元的有限差分格式,并利用非线性Galerkin方法讨论该差分格式的稳定性。通过对该格式的稳定性分析,说明和古典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。The finite difference scheme with incremental unknowns for a higher dimensional nonlinear reaction-diffusion equation is presented by means of introducing incremental unknowns method and the stability of the scheme is discussed with nonlinear Galerkin method.Through stability analysis for the scheme,it was shown that stability of the finite difference scheme with the incremental unknowns is improved when compared with that of the corresponding classic difference scheme.

关 键 词：稳定性分析 增量未知元 有限差分 反应扩散方程 

分 类 号：O241.84[理学—计算数学]