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| 非线性常微分方程的Lie级数解法及其计算机代数实现 | |
| 引用本文： | 黄东卫,郑丽霞,魏育飞. 非线性常微分方程的Lie级数解法及其计算机代数实现[J]. 内蒙古工业大学学报, 2000, 19(1): 6-10 |
| 作者姓名： | 黄东卫 郑丽霞 魏育飞 |
| 作者单位： | [1]内蒙古工业大学基础部 [2]内蒙古河套大学理工部 |
| 基金项目： | 内蒙古自治区自然科学基金项目，内蒙古工业大学校科研基金项目． |
| 摘 要： | Ｌｉｅ级数是常微分方程的以初始条件为系数的幂级数解，它适于微分方程的性态的研究，并易于说明其对初始条件敏感的混沌性，在此利用Ｍａｔｈｅｍａｔｉｃａ繁育地此问题予以实现，给出产生ＯＤＥｓ的近似解析解的方法。 |
| 关 键 词： | 常微分方程 Lie级数 解法 非线性 |
| 文章编号： | 1001-5167(2000)01-0006-05 |
THE LIE-SERIES SOLUTION TO SYSTEMS OF NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS AND ITS ALGEBRAIC REALIZATION ON COMPUTER |
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| HUANG Dong-wei,ZHENG Li-xiaWEI Yu-fei. THE LIE-SERIES SOLUTION TO SYSTEMS OF NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS AND ITS ALGEBRAIC REALIZATION ON COMPUTER[J]. Journal of Inner Mongolia Polytechnic University(Social Sciences Edition), 2000, 19(1): 6-10 | |
| Authors: | HUANG Dong-wei ZHENG Li-xiaWEI Yu-fei |
| Affiliation: | HUANG Dong-wei,ZHENG Li-xia;(eaching Department of Basic Sciences,Inner Mongolia Polytechnic University,Hohhot 010062,PRC);WEI Yu-fei;(Department of Science and Technology,lnner Mongolia Hetao University,Linhe 015000,PRC) |
| Abstract: | The Lie-series is a power series in which the initial conditions are part of the constant coefficients of the series. This property makes the Lie-series appropriate for the study of systems of differential equations that are sensitive to initial conditions. We hereby present a Mathematica program capable of* handling systems of ODEs. Several examples for application of the program to linear andnon-linear problems are given. |
| Keywords: | ordinary differential equation (ODE) Lie-series Mathematica |
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