华东师范大学学报(自然科学版) ›› 2004, Vol. 2004 ›› Issue (4): 16-23.

• 数学 统计学 • 上一篇    下一篇

求解非线性时滞反应扩散方程的有限差分格式(英文)

张丽芳，王元明   

  1. 华东师范大学数学系，上海200062
  • 收稿日期:2003-01-15 修回日期:2003-10-23 出版日期:2004-12-25 发布日期:2004-12-25
  • 通讯作者: 张丽芳

A Finite Difference Scheme for Nonlinear Reaction-diffusion Equations with Time Delay

ZHANG Li-fang，WANG Yuan-ming   

  1. Department of Mathematics, East China Normal University，Shanghai 200062，China
  • Received:2003-01-15 Revised:2003-10-23 Online:2004-12-25 Published:2004-12-25
  • Contact: ZHANG Li-fang

摘要： 建立了一个用于求解非线性时滞反应扩散方程的有限差分格式，在空间和时间方向上该格式分别具有四阶和两阶精度，用上下解方法给出了有限差分解的存在和唯一性，建立了一个单调迭代用于计算有限差分解，数值结果显示了该方法的优越性.

关键词: 非线性反应扩散方程, 时滞, 有限差分格式, 高精度, 单调迭代, 非线性反应扩散方程, 时滞, 有限差分格式, 高精度, 单调迭代

Abstract: A finite difference scheme with the accuracy of fourth order in space and second order in time is proposed for solving a nonlinear reaction-diffusion equation with time delay. Existence and uniqueness of the solution is given by the method of upper and lower solutions. A monotone iteration is also developed for the computation of the finite difference solution. The convergence of the scheme is discussed. The numerical results shows the advantages of the method.

Key words: finite difference scheme, time Delay, monotone iteration, nonlinear reaction-diffusion equation, finite difference scheme, time Delay, monotone iteration

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