| 重正化群法在一类三阶奇异摄动问题中的应用 |
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| 引用本文： | 何晓莹.重正化群法在一类三阶奇异摄动问题中的应用[J].广西工学院学报,2006,17(3):13-16. |
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| 作者姓名： | 何晓莹 |
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| 作者单位： | 广西工学院,信息与计算科学系,广西,柳州,545006 |
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| 摘 要： | 物理和工程学中出现的很多问题都是通过奇异摄动问题来描述的,而这类问题的解对某些参数是不一致收敛的。重正化群方法已成为获得这类问题精确解的一致有效渐近展开式的有用工具。本文将重正化群方法应用到一类三阶奇异摄动初值问题中,构造出了该问题的一致有效的渐近展开式,该方法比传统的方法更简单有效。
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| 关 键 词： | 重正化群 奇异摄动 一致渐近有效展式 |
| 文章编号： | 1004-6410（2006）03-0013-04 |
| 收稿时间： | 2006-05-25 |
| 修稿时间： | 2006年5月25日 |
Renormalization group theory applied in a kind of three order singular perturbation problems |
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| HE Xiao-ying.Renormalization group theory applied in a kind of three order singular perturbation problems[J].Journal of Guangxi University of Technology,2006,17(3):13-16. |
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| Authors: | HE Xiao-ying |
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| Affiliation: | Department of Information and Computing Science, Guangxi University of Technology, Liuzhou 545006, China |
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| Abstract: | Many problems in physics and engineering are described by singular perturbation problems.However,the solutions to this kind of problems are not uniformly convergent for some parameters.Renormalization group method is an effective tool to obtain the uniformly valid asymptotic expansion exact solutions of this kind of problems.In this paper,we illustrate the application of renormalization group method into a kind of initial value problems of three order singular perturbation and construct the uniformly valid asymptotic expansion for these problems.This method is simpler and more effective than traditional method. |
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| Keywords: | renormalization group theory singular perturbation problems uniformly valid asymptotic expansion |
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