华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (5): 34-42.

• 数学 统计学 • 上一篇    下一篇

具有扩散的自助模型的有限差分解(英)

管秋琴1,2, 王元明1   

  1. 1.华东师范大学 数学系, 上海 200062; 2.上海电力学院 数理系, 上海 200090
  • 收稿日期:2005-03-07 修回日期:2005-11-29 出版日期:2006-09-25 发布日期:2012-11-27

Finite Difference Solutions of a Cooperative Model with Diffusion

GUAN Qiu-qin1,2, WANG Yuan-ming1   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, China; 2. Department of Mathematics and Physics, Shanghai University of Electric Power, Shanghai200090, China
  • Received:2005-03-07 Revised:2005-11-29 Online:2006-09-25 Published:2012-11-27

摘要： 研究具有扩散的自助模型的有限差分解. 首先建立一个单调迭代格式用于求解有限差分方程组;
然后讨论非负解的存在唯一性, 对不同的参数,证明方程组有四种不同类型的非负解,且这些非负解可以通过选择合适的初始迭代由迭代格式计算而得到; 最后给出一些数值结果.

关键词: 自助模型, 有限差分方程组, 非负解, 单调迭代 ,  ,

Abstract: This paper studied the finite difference solutions of a cooperative model with diffusion. A monotone iterative scheme was developed for solving the nonlinear finite difference system. The existence and uniqueness of a nonnegative solution was investigated. It was shown that the system may have four types of
nonnegative solutions for different parameters, and each of these solutions could be computed by a suitable choice of initial iteration in the monotone iterative scheme. Some numerical results were given.

Key words: cooperative model, finite difference system, nonnegative solution, monotone iteration  ,

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