任意凸四边形区域上二阶椭圆特征值问题基于高斯点的一种有效的谱配置法  

An Efficient Spectral Collocation Method Based on Gaussian Points for Second Order Elliptic Eigenvalue Problems on Arbitrary Convex Quadrilateral Domains

作　　者：郑继会 王远路 ZHENG Ji-Hui;WANG Yuan-lu(School of Mathematical Sciences,Guizhou Normal University,Guiyang 550025)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《遵义师范学院学报》2023年第5期91-95,共5页Journal of Zunyi Normal University

摘　　要：作者提出了任意凸四边形区域上基于高斯点的二阶椭圆特征值问题的一种有效谱配置法.该方法首先利用等参变换将任意凸四边形区域上的函数转化为[-1,1]×[-1,1]上的函数,然后根据边界条件,可根据Legendre多项式的正交性构造一组有效的基函数,将数值解表示为这组基函数的展开组合.再次,通过编程计算出每个基函数在这些高斯点上的节点值,将离散格式推导为一个线性的矩阵特征系统.最后,给出了一些数值算例来表明算法的正确性和有效性,数值结果表明了该方法是有效的和收敛的.In this paper,an efficient spectral collocation method based on Gaussian points is proposed for the second order elliptic eigenvalue problem in an arbitrary convex quadrilateral region.This method first uses isoparametric transformation to transform the function on an arbitrary convex quadrilateral region into a function on[-1,1]×[-1,1],then,based on the boundary conditions,a set of effective basis functions can be constructed according to the orthogonality of Legendre polynomials,and the numerical solution can be expressed as an expansion combination of this set of basis functions.Again,the node values of each basis function at these Gaussian points are calculated by programming,and the discrete format is derived into a linear matrix eigen-system.Finally,some numerical examples are given to demonstrate the correctness and effectiveness of the algorithm.The numerical results showthat the method is effective and convergent.

关 键 词：任意凸四边形区域 二阶椭圆特征值问题 高斯谱配置法 数值算例 

分 类 号：O241[理学—计算数学]