中文核心期刊
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重庆交通大学学报（自然科学版）

重庆交通大学学报（自然科学版） ›› 2000, Vol. 19 ›› Issue (2): 108-111.

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变系数二阶常微分方程的边界层型问题的插值摄动解法

袁镒吾1, 李永纯2, 徐积江2   

  1. 1. 中南工业大学, 长沙 410083;
    2. 江西省赣州公路分局, 江西赣州 341000
  • 收稿日期:1999-05-17 修回日期:1999-07-13 出版日期:2000-04-22 发布日期:2016-11-08
  • 作者简介:袁镒吾(1929一),男,湖南隆回人,中南工业大学教授,近期从事奇异摄动理论研究

Interpolation perturbation method for solving boundary layer type problems of second order ordinary differential eguations with variable coefficients

YUAN Yi-wu1, LI Yong-chun2, XU Ji-jiang2   

  1. 1. Centralsouth University, Changsha 410083, CHina;
    2. Jiangxi Highway Managing Office, Ganzhou Bureau, Ganzhou Jiangxi 314000, China
  • Received:1999-05-17 Revised:1999-07-13 Online:2000-04-22 Published:2016-11-08

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摘要： 用插值摄动法[1]求得了变系数二阶常微分方程的边界层型问题的一级近似解.由于该方法能公式化(如式(10)),故其计算过程显得十分简便.其精度甚至比多尺度法的还稍高一些.

关键词: 变系数, 微分方程, 边界层, 插值, 摄动法

Abstract: In this paper, by using the interpolation perturbation method, the authors obtain the first order approximate solutions of the boundary layer type problems of the second order ordinary differential equations with variable coefficients. Since the method of this paper may be formularized (See Eq. (10)), the calculating process of this paper is quite simple and its accuracy its accuracy is even higher than that of the multiple scales method.

Key words: variable coefficient, differential equation, boundary layer, interpolation, perturbation method

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