| 一类微分方程广义特征值的算法 |
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| 引用本文： | 陈静,顾晨宇,钱椿林.一类微分方程广义特征值的算法[J].苏州科技学院学报(自然科学版),2006,23(2):9-13. |
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| 作者姓名： | 陈静 顾晨宇 钱椿林 |
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| 作者单位： | 苏州市广播电视大学,江苏,苏州,215004 |
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| 摘 要： | 考虑计算一类微分方程广义特征值的近似值的算法。运用泛函证明了三个引理；采用Galerkin方法来构造适当的基函数，并利用Cauchy不等式给出了其特征值计算的误差估计式；并得到该问题的算法。此算法可以用第n次近似值来估计第n-1次的近似值的精确度，并给出了应用实例。
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| 关 键 词： | 微分方程 广义特征值 特征函数 Galerkin方法 |
| 文章编号： | 1672-0687（2006）02-0009-05 |
| 收稿时间： | 2005-08-20 |
| 修稿时间： | 2005-08-20 |
A Computational Method for the Generalized Eigenvalues of a Certain Class of the Differential Equation |
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| CHEN Jing,GU Chen-yu,QIAN Chun-lin.A Computational Method for the Generalized Eigenvalues of a Certain Class of the Differential Equation[J].Journal of University of Science and Technology of Suzhou,2006,23(2):9-13. |
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| Authors: | CHEN Jing GU Chen-yu QIAN Chun-lin |
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| Institution: | Suzhou Radio and Television University, Suzhou 215004, China |
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| Abstract: | This paper provides a computational method of the approximate value of the generalized eigenvalues for a certain class of the differential equation.Three lemmas are proved on the basis of the functional analysis.The primary functions are made by Galerkin method,and the error estimates of eignevalues are given by Cauchy inequality.The computational method of the approximate value of the eigenvalues is obtained.The accuracy of(n-1)-th approximate value is estimated by n-th approximate value.At last,an applied example is given. |
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| Keywords: | differential equation generalized eigenvalue eigenfunction Galerkin method |
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