| 用无限阶矩阵求微分方程在奇点处的级数解 |
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| 引用本文： | 李大林,吕显瑞. 用无限阶矩阵求微分方程在奇点处的级数解[J]. 吉林大学学报(理学版), 2007, 45(2): 203-207 |
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| 作者姓名： | 李大林 吕显瑞 |
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| 作者单位： | 吉林大学,数学研究所,长春,130012;柳州职业技术学院,基础部,广西壮族自治区,柳州,545006;吉林大学,数学研究所,长春,130012 |
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| 基金项目： | 高等学校博士学科点专项科研项目 |
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| 摘 要： | 应用线性微分算子在幂基下的无限阶矩阵, 研究线性微分方程在奇点处的级数解. 得到一个计算无限阶矩阵属于零的特征向量的递推公式, 进而用这些特征向量表示级数解. 给出用有限阶矩阵判断奇点正则性的方法, 并改进了Fuchs定理.
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| 关 键 词： | 常微分方程 无限阶矩阵 特征向量 级数解 正则奇点 |
| 文章编号： | 1671-5489(2007)02-0203-05 |
| 收稿时间： | 2006-06-26 |
| 修稿时间： | 2006-06-26 |
Series Solutions of Linear Ordinary Differential Equation at Singular Point by Infinite Order Matrix |
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| LI Da-lin,L Xian-rui. Series Solutions of Linear Ordinary Differential Equation at Singular Point by Infinite Order Matrix[J]. Journal of Jilin University: Sci Ed, 2007, 45(2): 203-207 |
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| Authors: | LI Da-lin L Xian-rui |
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| Affiliation: | 1. Institute of Mathematics, Jilin University, Changchun 130012, China; 2. Department of Foundation,Liuzhou Vocational Institute of Technology, Liuzhou 545006, Guangxi Zhuang Autonomous Region, China |
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| Abstract: | The series solutions of the linear ordinary differential equation at singular point were studied via the infinite order matrix of the linear differential operator in power series basis. We got a recurrence formula to compute the characteristic vectors of the infinite order matrix belonging to λ=0 and then completed the expression of the series solutions with the characteristic vectors. The regularity of singular point is judged with a finite order matrix, and the Fuchs theorem has been improved. |
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| Keywords: | ordinary differential equation infinite order matrix characteristic vector series solution regular singular point |
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