华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (6): 46-56.

• 应用数学与基础数学 • 上一篇    下一篇

求解具有脉冲状空间对照结构的奇异摄动问题的边值方法

宋 慈   

  1. 华东师范大学 地理信息科学重点实验室, 上海 200241
  • 收稿日期:2012-11-01 修回日期:2013-03-01 出版日期:2013-11-25 发布日期:2014-01-13

Boundary value apaproach to solve a class of singularly perturbed problems with spike-type contrast structure

SONG Ci   

  1. Key Laboratory of Geographic Information Science, East China Normal University, Shanghai 200241, China
  • Received:2012-11-01 Revised:2013-03-01 Online:2013-11-25 Published:2014-01-13

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摘要： 通过采用边值方法求解具有脉冲状空间对照结构的奇异摄动边值问题.
对于内部层问题, 先从内部层转移点~$t^*$~处将原问题划分为左右两个问题,
再通过边值方法可以得到分别相应于左右问题的非奇异摄动方程.
对于边界层问题, 可以直接通过边值方法得到相应的非奇异摄动方程. 最后,
通过数值试验证明了边值方法的有效性.

关键词: 边值方法, 奇异摄动, 内部层, 边界层, 脉冲解

Abstract: For the internal layer problem, firstly, the original
problem was partitioned into left and right problems from the
transfer point at the internal layer region. Then, through the
boundary value method, the left and right problems were converted
into non-singularly perturbed problems. And by boundary layer
correction technique, the original problem was directly converted
into two non-singularly perturbed problems. Lastly, the efficiency
of the boundary value method could be indicated by numerical tests.

Key words: boundary value method, singular perturbation, internal layer, boundary layer, spike-type solution

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