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） ›› 1999, Vol. 18 ›› Issue (3): 110-114.

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一类弱非线性常微分方程的插值摄动解法

袁镒吾1, 李永纯2, 徐积江2   

  1. 1. 中南工业大学, 湖南长沙 410083;
    2. 江西省赣州公路分局, 江西赣州 341000
  • 收稿日期:1998-12-08 修回日期:1999-01-21 出版日期:1999-06-22 发布日期:2016-10-31
  • 作者简介:袁镒吾(1929-),男,中南工业大学教授,近期研究奇异摄动理论.

The Interpolation Perturbation Method for Solving A Class of Weakly Nonlinear Differential Equations

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

  1. 1. Central South University of Technology, Changsha 410083, China;
    2. Jiangxi Highway Managing Office Ganzhou Bureau, Ganzhou Jiangxi 341000, China
  • Received:1998-12-08 Revised:1999-01-21 Online:1999-06-22 Published:2016-10-31

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摘要： 用插值摄动法[1]研究一类弱非线性常微分方程的初值问题,得到了一级及二级近似解.解的精度很高,并逐级提高.如果用正则摄动法求解此类问题,则当自变量较大时,误差很大.

关键词: 插值摄动法, 正则摄动法, 高阶近似

Abstract: In this paper, the authors study the initial value problems of a class of weakly nonlinear differential equation.The first and the second order approximate solutions are obtained.Their accuracies are high and the more the approximate order is high, the more the accuracy is high.If the regular perturbation method is used to solve the same problems, then, when the independent variable is big, so is the error of the solution.

Key words: interpolation perturbation method, regular perturbation method, high approximate order

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