| 特征值问题的应用简述 |
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| 引用本文： | 姜亦成,樊红云. 特征值问题的应用简述[J]. 高等数学研究, 2022, 25(1): 69-70,95. DOI: 10.3969/j.issn.1008-1399.2022.01.022 |
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| 作者姓名： | 姜亦成 樊红云 |
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| 作者单位： | 齐齐哈尔大学理学院,黑龙江齐齐哈尔161006 |
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| 基金项目： | 齐齐哈尔大学博士科研基金启动项目;黑龙江省教育厅基本科研业务专项 |
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| 摘 要： | 从矩阵的特征问题入手,引出常系数线性齐次微分方程求解的特征方程方法;利用分离变量法求解热传导方程,引入拉普拉斯方程的特征问题,给出求解过程,并给出热方程的解的渐近稳定性.
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| 关 键 词： | 特征值 特征向量 特征函数 线性微分方程 热方程 渐近稳定性 |
An Introduction to Application of the Eigenvalue Problem |
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| JIANG Yicheng,FAN Hongyun. An Introduction to Application of the Eigenvalue Problem[J]. Studies In College Mathematics, 2022, 25(1): 69-70,95. DOI: 10.3969/j.issn.1008-1399.2022.01.022 |
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| Authors: | JIANG Yicheng FAN Hongyun |
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| Affiliation: | (College of Science, Qiqihar University, Qiqihaer 161006, China) |
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| Abstract: | In this paper,we begin with the eigenvalue problem for matrix,and follow by the use of the characteristic equation to solve linear homogeneous differential equation with constant coefficients.To find the solution for heat equation with the method of separating variables,we introduce and solve the eigenvalues of Laplace equation.Finally,we obtain the asymptotic stability of the solution for heat equation. |
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| Keywords: | eigenvalue eigenvector eigen-function linear differential equation heat equation asymptotic stability |
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