自共轭常微分算子特征值的一种基于分离特征参数的数值解法

数学物理学报 ›› 2012, Vol. 32 ›› Issue (1): 55-67.

自共轭常微分算子特征值的一种基于分离特征参数的数值解法

陈金设, 孙炯

内蒙古大学数学科学学院呼和浩特 010021

收稿日期:2009-12-22 修回日期:2011-03-07 出版日期:2012-02-25 发布日期:2012-02-25
基金资助:
国家自然科学基金(10561005, 10861008)和内蒙古大学高层次人才引进科研启动项目(Z20090117)资助

Numerical Computation of Eigenvalues of Self-adjoint Differential Operators by Using the Method of Separating Eigen-parameter

CHEN Jin-She, SUN Jiong

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021

Received:2009-12-22 Revised:2011-03-07 Online:2012-02-25 Published:2012-02-25
Supported by:
国家自然科学基金(10561005, 10861008)和内蒙古大学高层次人才引进科研启动项目(Z20090117)资助

摘要/Abstract

摘要：

该文发现了特征方程 ly(x, λ) = λy(x, λ) 一般解的一种关于特征参数λ 的幂级数表示及其求解方法, 借此给出了自共轭常微分算子特征值的一种新的数值解法, 并给出了算法的稳定性分析和误差估计. 最后,
通过数值实例来说明该算法是有效的.

关键词: 常微分算子, 特征值, 数值计算, 分离特征参数, 特征行列式

Abstract:

In this paper, a power series representation in λ and its method to solve for the general solution of eigen-equation ly(x, λ) = λy(x, λ) are discovered. Then, a new numerical method to get eigenvalues of self-adjoint ordinary di?erential operators is obtained. Also the analysis of stability and error for the algorithm are given. At last, the numerical examples are presented to verify the effciency of the method.

Key words: Ordinary differential operators, Eigenvalues, Numerical computation, Separating eigen-parameter, Eigen-determinant

中图分类号:

34L16

陈金设, 孙炯. 自共轭常微分算子特征值的一种基于分离特征参数的数值解法[J]. 数学物理学报, 2012, 32(1): 55-67.

CHEN Jin-She, SUN Jiong. Numerical Computation of Eigenvalues of Self-adjoint Differential Operators by Using the Method of Separating Eigen-parameter[J]. Acta mathematica scientia,Series A, 2012, 32(1): 55-67.

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