一阶常微分方程组的奇异摄动问题

J4 ›› 2009, Vol. 47 ›› Issue (05): 941-944.

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Singular Perturbation Problems for First OrderOrdinary Differential Equations

ZHOU Ran¹, ZHANG Yanni², Hwang Gyongnam³

1. Mathematics Section| Department of Agriculture| |Jilin University, Changchun 130062, China;2. Institute of Mathematics, Jilin University, Changchun 130012, China|3. Department of Mathematics, D. P. R. K Kim Hyong Jik University of Education, PyongYang 999093, D.P.R.K

Received:2009-01-04 Online:2009-09-26 Published:2009-11-03
Contact: ZHOU Ran E-mail:zhouranjlu@yahoo.cn.

Abstract

Abstract:

Combining the stretched coordinate method with the multiple scales method, we constructed the uniformly valid expansion for the singular perturbation problems of first order ordinary differential equations. Furthermore, to show the validness of our result, we applied our method to the Duffing equation and obtained the uniformly valid asymptotic expansions.

Key words: singular perturbation, stretched coordinate method, multiple scales method, Duffing equation

CLC Number:

O175

ZHOU Dan, ZHANG Yan-Ni, HUANG Jing-Nan. Singular Perturbation Problems for First OrderOrdinary Differential Equations[J].J4, 2009, 47(05): 941-944.

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Singular Perturbation Problems for First OrderOrdinary Differential Equations

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