摘要
构建了计算某类六阶微分方程带权特征值的近似值的算法。主要结果的证明基于变分原理。首先证明了三个引理;其次采用Galerkin方法来构造适当的基函数,利用Cauchy不等式给出了其特征值计算的误差估计式;最后得到计算某类六阶微分方程带权特征值的近似值的算法,而且可以用第n次近似值来估计第n-1次的近似值的精确度。只要适当选取n,就可以求得所要精确度的特征值的近似值,这个算法具有广泛的实用价值和理论价值。
One computational method of the approximate values of the weighted eigenvalues for a certain class of differential equation of the sixth order is suggested.The related proof is based on the variational formula.Firstly,three lemmas are proved.Secondly,the basis functions are chosen in terms of Galerkin method,and the formulas for the error estimates of eignevalues are given by Cauchy inequality.At last,the computational method of the approximate values of the eigenvalues was found,and the accuracy of the (n-1)-th approximate value is dependent on the n-th approximate value.If only n is appropriately selected,the expected accuracy of eigenvalues is reached.This computational method is of definite significance both in application and in theory.
出处
《江苏广播电视大学学报》
2004年第3期28-30,共3页
Journal of Jiangsu Radio & Television University
关键词
某类六阶微分方程
权
特征值
特征函数
GALERKIN方法
a certain class of differential equation of the sixth order
weight
eigenvalue
eigenfuction
Galerkin method
