一类线性奇异边值问题的谱配置方法  

Spectral Collocation Method for a Class of Linear Singular Boundary Value Problems

作　　者：王天军[1] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471023

出　　处：《河南科技大学学报（自然科学版）》2013年第6期75-78,8,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11171227);河南省教育厅自然科学基金项目(2011B110014);河南科技大学博士启动基金项目(09001263)

摘　　要：对一类具有正则奇点的线性常微分方程奇异边值问题进行了正则化处理,利用Jacobi-Gauss-Lobatto节点为配置点,用谱配置方法求其数值解,逼近问题的正确解。给出算法格式和相应的数值试验结果,证明所提算法格式的有效性和高精度。所用方法可用于求解奇点阶数为任意正数的正则奇点的情况。This paper deals with the numerical solutions of a class of linear singular boundary value problems defined on bounded interval by regularization method and spectral-collocation method that approximate the exact solution of the singular boundary value problem. Jacobi-Gauss-Lobatto nodes were used to collocate nodes. Efficient algorithms were implemented. Numerical results demonstrate its efficiency and high accuracy of the approach. The proposed method can be used to the cases that the singularity order of regular singular point is an arbitrary positive number.

关 键 词：常微分方程 奇异边值问题 谱配置方法 Jacobi-Gauss-Lobatto节点 

分 类 号：O175.2[理学—数学]