数学季刊 ›› 2008, Vol. 23 ›› Issue (2): 222-227.

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一类非线性反应-扩散方程有限差分格式的稳定性研究

  

  1. College of Mathematics and Information Science,Henan University

  • 收稿日期:2007-03-27 出版日期:2008-06-30 发布日期:2023-10-07
  • 作者简介: XU Chen-mei (1965-), female, native of Zhoukou, Henan, a lecturer of Henan University, engages in computational mathematics.

The Stability Research for the Finite Difference Scheme of a Nonlinear Reaction-diffusion Equation 

  1. College of Mathematics and Information Science,Henan University
  • Received:2007-03-27 Online:2008-06-30 Published:2023-10-07
  • About author: XU Chen-mei (1965-), female, native of Zhoukou, Henan, a lecturer of Henan University, engages in computational mathematics.

摘要: In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristic in gaining the stability condition of the scheme.

关键词: reaction-diffusion equation, finite difference scheme, stability research, variational approximation method

Abstract: In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristic in gaining the stability condition of the scheme.

Key words: reaction-diffusion equation, finite difference scheme, stability research, variational approximation method

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