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

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

详细信息

中图分类号: O157.5
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出版历程
- 收稿日期: 2012-11-01
- 修回日期: 2013-03-01
- 刊出日期: 2013-11-25

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

摘要

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.
- 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.
- boundary value method /
- singular perturbation /
- internal layer /
- boundary layer /
- spike-type solution

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参考文献(1)

[1]

{1} MOBAN K, KADALBAJOO, REDDY Y N. A boundary value method for a class of nonlinear singular perturbation problem [J]. Appl. Numer. 1988, 4:587-594.
{2} KUMAR M, MISHRA H K, SINGH P. A boundary value approach for a class of linear singularly perturbed boundary value problems [J]. Adva. Engi. Soft. 2009, 40:298-304.
{3} PLAK R C, MIHRELOV A C. 在非均匀化学物理中的自组织化过程[M]. 莫斯科: 莫斯科科学出版社, 1983.
{4} ROMANOVSHGE U M, SJTEGANOV M B, CHRONOVSHGE D C, 数学的生物物理[M]. 莫斯科: 莫斯科科学出版社, 1984.
{5} 倪明康, 林武忠. 奇异摄动问题中的渐近理论[M]. 北京: 高等教育出版社, 2008.
{6} 倪明康, 林武忠. 奇异摄动方程解的渐近展开[M]. 北京: 高等教育出版社, 2008.
{7} 王爱峰, 倪明康. 二阶非线性奇摄动方程脉冲状空间对照结构[J]. 数学物理学报, 2009.
{8} 陈丽华, 徐洁, 倪明康. 一类三阶非线性常微分方程的奇摄动边值问题[J]. 华东师范大学学报\,(自然科学版), 2008(3): 0012-09.
{9} XIE F, WANG J, ZHANG W J, HE M. A novel method for a class of parameterized singularly perturbed boundary value problems [J]. Comput. Appl. Math. 2008, 213: 258-267.
{10} KUMAR M, SINHG P, MISHRA H K. A recent survey on computational techniques for solving singularly perturbed boundary value problems[J]. Int J Comput Math 2007, 84: 1439-1463.
{11} VIGO-AGUIAR J, NATESAN S. An efficient numerical method for singualar perturbation problems [J]. Comput Appl Math. 2006, 190: 287-303.

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