用范式理论研究常微分方程焦点量问题*
Studying the Focal Value of Ordinary Differential Equations by Normal Form Theory
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摘要: 利用范式与焦点量之间关系的一个定理并拓展了矩阵表示法,借助于计算机代数语言Mathe-matica的帮助,本文给出了一种计算常微分方程焦点量问题的新方法,利用这种方法可以计算常微分方程的任意阶焦点量,并通过一个算例验证了本文所提出的方法的正确性。这种方法的优点是简捷、方便、只进行简单的代数运算。
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关键词:
- 范式 /
- 常微分方程 /
- 焦点量 /
- Mathematica
Abstract: We present a new method to calculate the focal value of ordinary differential equation by applying the theorem defined the relationship between the normal form and focal value,with the help of a symbolic computation language MATHE-MATICA,and extending the matrix representation method.This method can be used to calculate the focal value of any high order terms.This method has been verified by an example.The advantage of this method is simple and more readily applicable.the result is directly obtained by substitution.-
Key words:
- normal form /
- ordinary differential equation /
- focal value /
- Mathematica
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