四阶椭圆特征值问题的有效谱Galerkin方法  

An Effective Spectral Method Based on the Legendre-Galerkin Approximation for Fourth Order Ellipse Eigenvalue Problem

作　　者：李艳琴[1,2] 安静[3] 

机构地区：[1]贵州师范学院数学与计算机科学学院,贵州贵阳550018 [2]贵州师范学院贵州省高校工业物联网工程技术研究中心,贵州贵阳550018 [3]贵州师范大学数学与计算机科学学院,贵州贵阳550001

出　　处：《四川师范大学学报（自然科学版）》2015年第2期249-254,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：贵阳市科技计划(筑科合同[2013101]10-6号)资助项目

摘　　要：给出四阶椭圆特征值问题基于Legendre-Galerkin逼近的有效的谱方法,首先选择一组适当的基函数,使得离散变分格式的矩阵形式尽可能是稀疏的,然后分别在二维和三维情况下推导离散变分格式基于张量积的矩阵形式,通过利用矩阵分解能够迅速地求出特征值和特征向量,并作出误差估计,最后给出数值算例,数值结果表明该方法是稳定的和有效的.In this paper,we give an effective spectral method based on the Legendre-Galerkin approximation for fourth order ellipse eigenvalue problem. We first choose an appropriate set of basis functions such that the matrices in the discrete variational form are sparse as far as possible. Then we deduce the matrix formulations based on the tensor-product for the discrete variational form in two and three-dimensional cases,respectively. By using matrix decomposition we can compute the discrete eigenvalues and eigenvectors rapidly. In addition,we also provide an error estimation and some numerical experiments. The numerical results indicate that our method is stable and effective.

关 键 词：四阶特征值问题 Legendre-Galerkin逼近 张量积 误差估计 

分 类 号：O241.82[理学—计算数学]