中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (6): 12-15.

• 研究论文 • 上一篇    下一篇

一类高维非线性反应扩散方程有限差分格式的稳定性

徐琛梅,于吉亮, 王 波   

  1. (河南大学数学与信息科学学院,河南 开封 475001)
  • 收稿日期:2010-12-25 修回日期:1900-01-01 出版日期:2011-11-25 发布日期:2011-11-25

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

XU Chenmei, YU Jiliang, WANG Bo

  

  1. (College of Mathematics and Information Science, Henan University, Kaifeng 475001, China)
  • Received:2010-12-25 Revised:1900-01-01 Online:2011-11-25 Published:2011-11-25

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。

关键词: 稳定性分析, 增量未知元, 有限差分, 反应扩散方程

Abstract: 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.

Key words: stability analysis, incremental unknowns, finite difference, reactiondiffusion equation

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